Theorem ori 642

Description: Infer implication from disjunction. (Contributed by NM, 11-Jun-1994.) (Revised by Mario Carneiro, 31-Jan-2015.)

Hypothesis

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

Assertion

Ref	Expression
ori	|- ( -. ph -> ps )

Proof of Theorem ori

Step	Hyp	Ref	Expression
1		ori.1	. 2 |- ( ph \/ ps )
2		pm2.53 641	. 2 |- ( ( ph \/ ps ) -> ( -. ph -> ps ) )
3	1, 2	ax-mp 7	1 |- ( -. ph -> ps )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  3ori  1195  mtpor  1316  ax-12  1402  sbal1yz  1877  dvelimALT  1886  dvelimfv  1887