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Theorem nfccdeq 2756
Description: Variation of nfcdeq 2755 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 2169 . . 3 x z A
3 equid 1586 . . . . 5 z = z
43cdeqth 2745 . . . 4 CondEq(x = yz = z)
5 nfccdeq.2 . . . 4 CondEq(x = yA = B)
64, 5cdeqel 2754 . . 3 CondEq(x = y → (z Az B))
72, 6nfcdeq 2755 . 2 (z Az B)
87eqriv 2034 1 A = B
Colors of variables: wff set class
Syntax hints:   = wceq 1242   wcel 1390  wnfc 2162  CondEqwcdeq 2741
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164  df-cdeq 2742
This theorem is referenced by: (None)
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