Theorem cdeqri 2801

Description: Property of conditional equality. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
cdeqri.1	|- CondEq ( x = y -> ph )

Assertion

Ref	Expression
cdeqri	|- ( x = y -> ph )

Proof of Theorem cdeqri

Step	Hyp	Ref	Expression
1		cdeqri.1	. 2 |- CondEq ( x = y -> ph )
2		df-cdeq 2799	. 2 |- (CondEq ( x = y -> ph ) <-> ( x = y -> ph ) )
3	1, 2	mpbi 143	1 |- ( x = y -> ph )

Syntax hints:   -> wi 4  CondEqwcdeq 2798

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104

This theorem depends on definitions:  df-bi 115  df-cdeq 2799

This theorem is referenced by:  cdeqnot  2803  cdeqal  2804  cdeqab  2805  cdeqal1  2806  cdeqab1  2807  cdeqim  2808  cdeqeq  2810  cdeqel  2811  nfcdeq  2812