Theorem orfa2

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

	Ref	Expression
Hypothesis	orfa2.1	|- ( ph -> F. )
Assertion	orfa2	|- ( ( ph \/ ps ) -> ps )

Proof

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