Theorem pm5.16 737

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		pm5.19 622	. 2 |- -. ( ps <-> -. ps )
2		simpl 102	. . 3 |- ( ( ( ph <-> ps ) /\ ( ph <-> -. ps ) ) -> ( ph <-> ps ) )
3		simpr 103	. . 3 |- ( ( ( ph <-> ps ) /\ ( ph <-> -. ps ) ) -> ( ph <-> -. ps ) )
4	2, 3	bitr3d 179	. 2 |- ( ( ( ph <-> ps ) /\ ( ph <-> -. ps ) ) -> ( ps <-> -. ps ) )
5	1, 4	mto 588	1 |- -. ( ( ph <-> ps ) /\ ( ph <-> -. ps ) )

Syntax hints:   -. wn 3   /\ wa 97   <-> 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: (None)