Theorem jaoian 785

Description: Inference disjoining the antecedents of two implications. (Contributed by NM, 23-Oct-2005.)

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 114	. . 3 |- ( ph -> ( ps -> ch ) )
3		jaoian.2	. . . 4 |- ( ( th /\ ps ) -> ch )
4	3	ex 114	. . 3 |- ( th -> ( ps -> ch ) )
5	2, 4	jaoi 706	. 2 |- ( ( ph \/ th ) -> ( ps -> ch ) )
6	5	imp 123	1 |- ( ( ( ph \/ th ) /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 103   \/ wo 698

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  ordi  806  ccase  954  xaddnemnf  9793  xaddnepnf  9794  faclbnd  10654  faclbnd3  10656