Theorem cdeqnot 2752

Description: Distribute conditional equality over negation. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
cdeqnot.1	|- CondEq ( x = y -> ( ph <-> ps ) )

Assertion

Ref	Expression
cdeqnot	|- CondEq ( x = y -> ( -. ph <-> -. ps ) )

Proof of Theorem cdeqnot

Step	Hyp	Ref	Expression
1		cdeqnot.1	. . . 4 |- CondEq ( x = y -> ( ph <-> ps ) )
2	1	cdeqri 2750	. . 3 |- ( x = y -> ( ph <-> ps ) )
3	2	notbid 592	. 2 |- ( x = y -> ( -. ph <-> -. ps ) )
4	3	cdeqi 2749	1 |- CondEq ( x = y -> ( -. ph <-> -. ps ) )

Syntax hints:   -. wn 3   <-> wb 98  CondEqwcdeq 2747

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  df-cdeq 2748

This theorem is referenced by: (None)