Theorem orfa2 33887

Description: Remove a contradicting disjunct from an antecedent. (Contributed by Giovanni Mascellani, 15-Sep-2017.)

Hypothesis

Ref	Expression
orfa2.1	|- ( ph -> F. )

Assertion

Ref	Expression
orfa2	|- ( ( ph \/ ps ) -> ps )

Proof of Theorem orfa2

Step	Hyp	Ref	Expression
1		orfa2.1	. . 3 |- ( ph -> F. )
2	1	orim1i 539	. 2 |- ( ( ph \/ ps ) -> ( F. \/ ps ) )
3		falim 1498	. . 3 |- ( F. -> ps )
4		id 22	. . 3 |- ( ps -> ps )
5	3, 4	jaoi 394	. 2 |- ( ( F. \/ ps ) -> ps )
6	2, 5	syl 17	1 |- ( ( ph \/ ps ) -> ps )

Syntax hints:   -> wi 4   \/ wo 383   F. wfal 1488

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-tru 1486  df-fal 1489

This theorem is referenced by: (None)