Theorem pm5.19 654

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 116	. . . 4 |- ( ( ph <-> -. ph ) -> ( ph -> -. ph ) )
2	1	pm2.01d 580	. . 3 |- ( ( ph <-> -. ph ) -> -. ph )
3		id 19	. . 3 |- ( ( ph <-> -. ph ) -> ( ph <-> -. ph ) )
4	2, 3	mpbird 165	. 2 |- ( ( ph <-> -. ph ) -> ph )
5	4, 2	pm2.65i 600	1 |- -. ( ph <-> -. ph )

Syntax hints:   -. wn 3   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  pm5.16  770  pclem6  1305  pm5.18im  1316  ru  2814