Theorem negel 33905

Description: An inference for negation elimination. (Contributed by Giovanni Mascellani, 24-May-2019.)

Hypotheses

Ref	Expression
negel.1	|- ( ps -> ch )
negel.2	|- ( ph -> -. ch )

Assertion

Ref	Expression
negel	|- ( ( ph /\ ps ) -> F. )

Proof of Theorem negel

Step	Hyp	Ref	Expression
1		negel.1	. . 3 |- ( ps -> ch )
2	1	adantl 482	. 2 |- ( ( ph /\ ps ) -> ch )
3		negel.2	. . 3 |- ( ph -> -. ch )
4	3	adantr 481	. 2 |- ( ( ph /\ ps ) -> -. ch )
5	2, 4	pm2.21fal 1505	1 |- ( ( ph /\ ps ) -> F. )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 384   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-an 386

This theorem is referenced by: (None)