
Implies[p,q]
represents the logical implication .


Implies 
Implies[p,q]
represents the logical implication .
Details

- As a Boolean function, Implies[p,q] is equivalent to
.
- Implies[p,q] can be input in StandardForm and InputForm as
. The character can be entered as
=>
or \[Implies].
Examples
open all close allScope (4)
Certain arguments automatically simplify:
Expand in terms of And, Or, and Not:
TraditionalForm formatting:
Applications (3)
Tech Notes
Related Guides
Related Links
History
Introduced in 1988 (1.0) | Updated in 1996 (3.0)
Text
Wolfram Research (1988), Implies, Wolfram Language function, https://reference.wolfram.com/language/ref/Implies.html (updated 1996).
CMS
Wolfram Language. 1988. "Implies." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/Implies.html.
APA
Wolfram Language. (1988). Implies. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Implies.html
BibTeX
@misc{reference.wolfram_2025_implies, author="Wolfram Research", title="{Implies}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/Implies.html}", note=[Accessed: 08-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_implies, organization={Wolfram Research}, title={Implies}, year={1996}, url={https://reference.wolfram.com/language/ref/Implies.html}, note=[Accessed: 08-August-2025]}