Theorem pm5.19 707

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 118	. . . 4 |- ( ( ph <-> -. ph ) -> ( ph -> -. ph ) )
2	1	pm2.01d 619	. . 3 |- ( ( ph <-> -. ph ) -> -. ph )
3		id 19	. . 3 |- ( ( ph <-> -. ph ) -> ( ph <-> -. ph ) )
4	2, 3	mpbird 167	. 2 |- ( ( ph <-> -. ph ) -> ph )
5	4, 2	pm2.65i 640	1 |- -. ( ph <-> -. ph )

Syntax hints:   -. wn 3   <-> 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 615  ax-in2 616

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm5.16  829  pclem6  1385  pm5.18im  1396  ru  2988  canth  5875  exmidonfinlem  7260