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Theorem cdeqab1 3153
 Description: Distribute conditional equality over abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
cdeqnot.1 CondEq
Assertion
Ref Expression
cdeqab1 CondEq
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem cdeqab1
StepHypRef Expression
1 cdeqnot.1 . . . 4 CondEq
21cdeqri 3147 . . 3
32cbvabv 2555 . 2
43cdeqth 3148 1 CondEq
 Colors of variables: wff set class Syntax hints:   wb 177   wceq 1652  cab 2422  CondEqwcdeq 3144 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-cdeq 3145
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