Theorem pm5.19 696

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		biimp 117	. . . 4 |- ( ( ph <-> -. ph ) -> ( ph -> -. ph ) )
2	1	pm2.01d 608	. . 3 |- ( ( ph <-> -. ph ) -> -. ph )
3		id 19	. . 3 |- ( ( ph <-> -. ph ) -> ( ph <-> -. ph ) )
4	2, 3	mpbird 166	. 2 |- ( ( ph <-> -. ph ) -> ph )
5	4, 2	pm2.65i 629	1 |- -. ( ph <-> -. ph )

Syntax hints:   -. wn 3   <-> wb 104

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-in1 604  ax-in2 605

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm5.16  818  pclem6  1364  pm5.18im  1375  ru  2950  canth  5796  exmidonfinlem  7149