Theorem pm5.16 813

Description: Theorem *5.16 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)

Assertion

Ref	Expression
pm5.16	|- -. ( ( ph <-> ps ) /\ ( ph <-> -. ps ) )

Proof of Theorem pm5.16

Step	Hyp	Ref	Expression
1		pm5.19 695	. 2 |- -. ( ps <-> -. ps )
2		simpl 108	. . 3 |- ( ( ( ph <-> ps ) /\ ( ph <-> -. ps ) ) -> ( ph <-> ps ) )
3		simpr 109	. . 3 |- ( ( ( ph <-> ps ) /\ ( ph <-> -. ps ) ) -> ( ph <-> -. ps ) )
4	2, 3	bitr3d 189	. 2 |- ( ( ( ph <-> ps ) /\ ( ph <-> -. ps ) ) -> ( ps <-> -. ps ) )
5	1, 4	mto 651	1 |- -. ( ( ph <-> ps ) /\ ( ph <-> -. ps ) )

Syntax hints:   -. wn 3   /\ wa 103   <-> 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 603  ax-in2 604

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)