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Theorem nfnae 1610
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 1607 . 2 𝑧𝑥 𝑥 = 𝑦
21nfn 1548 1 𝑧 ¬ ∀𝑥 𝑥 = 𝑦
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wal 1241  wnf 1349
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-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350
This theorem is referenced by:  sbequ6  1666  dvelimfv  1887  nfsb4t  1890
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