Theorem pm5.16 828

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		pm5.19 706	. 2 |- -. ( ps <-> -. ps )
2		simpl 109	. . 3 |- ( ( ( ph <-> ps ) /\ ( ph <-> -. ps ) ) -> ( ph <-> ps ) )
3		simpr 110	. . 3 |- ( ( ( ph <-> ps ) /\ ( ph <-> -. ps ) ) -> ( ph <-> -. ps ) )
4	2, 3	bitr3d 190	. 2 |- ( ( ( ph <-> ps ) /\ ( ph <-> -. ps ) ) -> ( ps <-> -. ps ) )
5	1, 4	mto 662	1 |- -. ( ( ph <-> ps ) /\ ( ph <-> -. ps ) )

Syntax hints:   -. wn 3   /\ wa 104   <-> 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 614  ax-in2 615

This theorem depends on definitions:  df-bi 117

This theorem is referenced by: (None)