Theorem jaoi3 1011

Description: Inference separating a disjunct of an antecedent. (Contributed by Alexander van der Vekens, 25-May-2018.)

Hypotheses

Ref	Expression
jaoi3.1	|- ( ph -> ps )
jaoi3.2	|- ( ( -. ph /\ ch ) -> ps )

Assertion

Ref	Expression
jaoi3	|- ( ( ph \/ ch ) -> ps )

Proof of Theorem jaoi3

Step	Hyp	Ref	Expression
1		jaoi3.1	. . 3 |- ( ph -> ps )
2		jaoi3.2	. . 3 |- ( ( -. ph /\ ch ) -> ps )
3	1, 2	jaoi 394	. 2 |- ( ( ph \/ ( -. ph /\ ch ) ) -> ps )
4	3	jaoi2 1010	1 |- ( ( ph \/ ch ) -> ps )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 383   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386

This theorem is referenced by:  2mpt20  6882  bropopvvv  7255  bropfvvvv  7257  ssnn0fi  12784  swrdnd  13432