Theorem imorr 711

Description: Implication in terms of disjunction. One direction of theorem *4.6 of [WhiteheadRussell] p. 120. The converse holds for decidable propositions, as seen at imordc 887. (Contributed by Jim Kingdon, 21-Jul-2018.)

Assertion

Ref	Expression
imorr	|- ( ( -. ph \/ ps ) -> ( ph -> ps ) )

Proof of Theorem imorr

Step	Hyp	Ref	Expression
1		ax-in2 605	. 2 |- ( -. ph -> ( ph -> ps ) )
2		ax-1 6	. 2 |- ( ps -> ( ph -> ps ) )
3	1, 2	jaoi 706	1 |- ( ( -. ph \/ ps ) -> ( 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:  pm4.52im  740  nf4r  1659