Theorem jaoian 425

Description: Inference disjoining the antecedents of two implications.

Hypotheses

Ref	Expression
jaoian.1	|- ((ph /\ ps) -> ch)
jaoian.2	|- ((th /\ ps) -> ch)

Assertion

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

Proof of Theorem jaoian

Step	Hyp	Ref	Expression
1		jaoian.1	. . . 4 |- ((ph /\ ps) -> ch)
2	1	ex 373	. . 3 |- (ph -> (ps -> ch))
3		jaoian.2	. . . 4 |- ((th /\ ps) -> ch)
4	3	ex 373	. . 3 |- (th -> (ps -> ch))
5	2, 4	jaoi 341	. 2 |- ((ph \/ th) -> (ps -> ch))
6	5	imp 350	1 |- (((ph \/ th) /\ ps) -> ch)

Syntax hints:   -> wi 3   \/ wo 222   /\ wa 223

This theorem is referenced by:  faclbnd 6882  faclbnd3 6884  faclbnd4lem1 6885  ipasslem3 8423  efifolem6 8642

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-or 224  df-an 225

Copyright terms: Public domain