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Theorem wl-nfae1 34649
Description: Unlike nfae 2447, this specialized theorem avoids ax-11 2151. (Contributed by Wolf Lammen, 26-Jun-2019.)
Assertion
Ref Expression
wl-nfae1 𝑥𝑦 𝑦 = 𝑥

Proof of Theorem wl-nfae1
StepHypRef Expression
1 aecom 2441 . 2 (∀𝑦 𝑦 = 𝑥 ↔ ∀𝑥 𝑥 = 𝑦)
2 nfa1 2146 . 2 𝑥𝑥 𝑥 = 𝑦
31, 2nfxfr 1844 1 𝑥𝑦 𝑦 = 𝑥
Colors of variables: wff setvar class
Syntax hints:  wal 1526  wnf 1775
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-10 2136  ax-12 2167  ax-13 2381
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-ex 1772  df-nf 1776
This theorem is referenced by:  wl-nfnae1  34650
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