Theorem mpan9 470

Description: Modus ponens conjoining dissimilar antecedents.

Hypotheses

Ref	Expression
mpan9.1	|- (ph -> ps)
mpan9.2	|- (ch -> (ps -> th))

Assertion

Ref	Expression
mpan9	|- ((ph /\ ch) -> th)

Proof of Theorem mpan9

Step	Hyp	Ref	Expression
1		mpan9.1	. . 3 |- (ph -> ps)
2	1	adantr 389	. 2 |- ((ph /\ ch) -> ps)
3		mpan9.2	. . 3 |- (ch -> (ps -> th))
4	3	adantl 388	. 2 |- ((ph /\ ch) -> (ps -> th))
5	2, 4	mpd 26	1 |- ((ph /\ ch) -> th)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  ghomgrpilem1 10319  ghomlin 10327  cnfilca 10487

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain