Theorem conimpfalt 41085

Description: Assuming a, not b, and a implies b, there exists a proof that a is false.) (Contributed by Jarvin Udandy, 29-Aug-2016.)

Hypotheses

Ref	Expression
conimpfalt.1	|- ph
conimpfalt.2	|- -. ps
conimpfalt.3	|- ( ph -> ps )

Assertion

Ref	Expression
conimpfalt	|- ( ph <-> F. )

Proof of Theorem conimpfalt

Step	Hyp	Ref	Expression
1		conimpfalt.3	. 2 |- ( ph -> ps )
2		conimpfalt.2	. 2 |- -. ps
3	1, 2	aibnbaif 41074	1 |- ( ph <-> F. )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   F. wfal 1488

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-tru 1486  df-fal 1489

This theorem is referenced by: (None)