Theorem jaoian 470

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 402	. . 3 |- (ph -> (ps -> ch))
3		jaoian.2	. . . 4 |- ((th /\ ps) -> ch)
4	3	ex 402	. . 3 |- (th -> (ps -> ch))
5	2, 4	jaoi 368	. 2 |- ((ph \/ th) -> (ps -> ch))
6	5	imp 377	1 |- (((ph \/ th) /\ ps) -> ch)

Syntax hints:   -> wi 3   \/ wo 239   /\ wa 240

This theorem is referenced by:  addgegt0i 6779  faclbnd 8197  faclbnd3 8199  faclbnd4lem1 8200  ipasslem3 9833  efifolem6 10081  bnj1139 12937

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 164  df-or 241  df-an 242

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