Theorem pm5.19 622

Description: Theorem *5.19 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)

Assertion

Ref	Expression
pm5.19	|- -. ( ph <-> -. ph )

Proof of Theorem pm5.19

Step	Hyp	Ref	Expression
1		bi1 111	. . . 4 |- ( ( ph <-> -. ph ) -> ( ph -> -. ph ) )
2	1	pm2.01d 548	. . 3 |- ( ( ph <-> -. ph ) -> -. ph )
3		id 19	. . 3 |- ( ( ph <-> -. ph ) -> ( ph <-> -. ph ) )
4	2, 3	mpbird 156	. 2 |- ( ( ph <-> -. ph ) -> ph )
5	4, 2	pm2.65i 568	1 |- -. ( ph <-> -. ph )

Syntax hints:   -. wn 3   <-> wb 98

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-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  pm5.16  737  pclem6  1265  pm5.18im  1276  ru  2763