Theorem pm5.18im 1385

Description: One direction of pm5.18dc 883, which holds for all propositions, not just decidable propositions. (Contributed by Jim Kingdon, 10-Mar-2018.)

Assertion

Ref	Expression
pm5.18im	|- ( ( ph <-> ps ) -> -. ( ph <-> -. ps ) )

Proof of Theorem pm5.18im

Step	Hyp	Ref	Expression
1		pm5.19 706	. 2 |- -. ( ps <-> -. ps )
2		bibi1 240	. . 3 |- ( ( ph <-> ps ) -> ( ( ph <-> -. ps ) <-> ( ps <-> -. ps ) ) )
3	2	notbid 667	. 2 |- ( ( ph <-> ps ) -> ( -. ( ph <-> -. ps ) <-> -. ( ps <-> -. ps ) ) )
4	1, 3	mpbiri 168	1 |- ( ( ph <-> ps ) -> -. ( ph <-> -. ps ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  xornbi  1386