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Theorem nfccdeq 2739
 Description: Variation of nfcdeq 2738 for classes. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypotheses
Ref Expression
nfccdeq.1 xA
nfccdeq.2 CondEq(x = yA = B)
Assertion
Ref Expression
nfccdeq A = B
Distinct variable groups:   x,B   y,A
Allowed substitution hints:   A(x)   B(y)

Proof of Theorem nfccdeq
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 nfccdeq.1 . . . 4 xA
21nfcri 2154 . . 3 x z A
3 equid 1571 . . . . 5 z = z
43cdeqth 2728 . . . 4 CondEq(x = yz = z)
5 nfccdeq.2 . . . 4 CondEq(x = yA = B)
64, 5cdeqel 2737 . . 3 CondEq(x = y → (z Az B))
72, 6nfcdeq 2738 . 2 (z Az B)
87eqriv 2019 1 A = B
 Colors of variables: wff set class Syntax hints:   = wceq 1228   ∈ wcel 1374  Ⅎwnfc 2147  CondEqwcdeq 2724 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-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004 This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-cleq 2015  df-clel 2018  df-nfc 2149  df-cdeq 2725 This theorem is referenced by: (None)
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