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Theorem wl-nfae1 34636
Description: Unlike nfae 2452, this specialized theorem avoids ax-11 2153. (Contributed by Wolf Lammen, 26-Jun-2019.)
Assertion
Ref Expression
wl-nfae1 𝑥𝑦 𝑦 = 𝑥

Proof of Theorem wl-nfae1
StepHypRef Expression
1 aecom 2446 . 2 (∀𝑦 𝑦 = 𝑥 ↔ ∀𝑥 𝑥 = 𝑦)
2 nfa1 2148 . 2 𝑥𝑥 𝑥 = 𝑦
31, 2nfxfr 1846 1 𝑥𝑦 𝑦 = 𝑥
Colors of variables: wff setvar class
Syntax hints:  wal 1528  wnf 1777
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-10 2138  ax-12 2169  ax-13 2385
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-ex 1774  df-nf 1778
This theorem is referenced by:  wl-nfnae1  34637
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