Theorem cdeqnot 2897

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 2895	. . 3 |- ( x = y -> ( ph <-> ps ) )
3	2	notbid 656	. 2 |- ( x = y -> ( -. ph <-> -. ps ) )
4	3	cdeqi 2894	1 |- CondEq ( x = y -> ( -. ph <-> -. ps ) )

Syntax hints:   -. wn 3   <-> wb 104  CondEqwcdeq 2892

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  df-cdeq 2893

This theorem is referenced by: (None)