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Theorem nfae 1623
Description: All variables are effectively bound in an identical variable specifier. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
nfae 𝑧𝑥 𝑥 = 𝑦

Proof of Theorem nfae
StepHypRef Expression
1 hbae 1622 . 2 (∀𝑥 𝑥 = 𝑦 → ∀𝑧𝑥 𝑥 = 𝑦)
21nfi 1367 1 𝑧𝑥 𝑥 = 𝑦
Colors of variables: wff set class
Syntax hints:  wal 1257  wnf 1365
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-nf 1366
This theorem is referenced by:  nfnae  1626  sbequ5  1681  a16nf  1762  dvelimfv  1903  dvelimor  1910  copsexg  4009
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