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Theorem nfnae 1685
Description: All variables are effectively bound in a distinct variable specifier. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
nfnae 𝑧 ¬ ∀𝑥 𝑥 = 𝑦

Proof of Theorem nfnae
StepHypRef Expression
1 nfae 1682 . 2 𝑧𝑥 𝑥 = 𝑦
21nfn 1621 1 𝑧 ¬ ∀𝑥 𝑥 = 𝑦
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wal 1314  wnf 1421
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 588  ax-in2 589  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-fal 1322  df-nf 1422
This theorem is referenced by:  sbequ6  1741  dvelimfv  1964  nfsb4t  1967
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