Theorem jaoa 709

Description: Inference disjoining and conjoining the antecedents of two implications. (Contributed by Stefan Allan, 1-Nov-2008.)

Hypotheses

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

Assertion

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

Proof of Theorem jaoa

Step	Hyp	Ref	Expression
1		jaao.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	adantrd 277	. 2 |- ( ph -> ( ( ps /\ ta ) -> ch ) )
3		jaao.2	. . 3 |- ( th -> ( ta -> ch ) )
4	3	adantld 276	. 2 |- ( th -> ( ( ps /\ ta ) -> ch ) )
5	2, 4	jaoi 705	1 |- ( ( ph \/ th ) -> ( ( ps /\ ta ) -> ch ) )

Syntax hints:   -> wi 4   /\ wa 103   \/ wo 697

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 698

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm4.79dc  888