Theorem imorri 739

Description: Infer implication from disjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Revised by Mario Carneiro, 31-Jan-2015.)

Hypothesis

Ref	Expression
imorri.1	|- ( -. ph \/ ps )

Assertion

Ref	Expression
imorri	|- ( ph -> ps )

Proof of Theorem imorri

Step	Hyp	Ref	Expression
1		imorri.1	. 2 |- ( -. ph \/ ps )
2		pm2.21 607	. . 3 |- ( -. ph -> ( ph -> ps ) )
3		ax-1 6	. . 3 |- ( ps -> ( ph -> ps ) )
4	2, 3	jaoi 706	. 2 |- ( ( -. ph \/ ps ) -> ( ph -> ps ) )
5	1, 4	ax-mp 5	1 |- ( ph -> ps )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 698

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-in2 605  ax-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)