Theorem jaoi2 1010

Description: Inference removing a negated conjunct in a disjunction of an antecedent if this conjunct is part of the disjunction. (Contributed by Alexander van der Vekens, 3-Nov-2017.) (Proof shortened by Wolf Lammen, 21-Sep-2018.)

Hypothesis

Ref	Expression
jaoi2.1	|- ( ( ph \/ ( -. ph /\ ch ) ) -> ps )

Assertion

Ref	Expression
jaoi2	|- ( ( ph \/ ch ) -> ps )

Proof of Theorem jaoi2

Step	Hyp	Ref	Expression
1		pm5.63 959	. 2 |- ( ( ph \/ ch ) <-> ( ph \/ ( -. ph /\ ch ) ) )
2		jaoi2.1	. 2 |- ( ( ph \/ ( -. ph /\ ch ) ) -> ps )
3	1, 2	sylbi 207	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:  jaoi3  1011