Users' Mathboxes Mathbox for Wolf Lammen < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  wl-nfae1 Structured version   Visualization version   GIF version

Theorem wl-nfae1 35309
Description: Unlike nfae 2433, this specialized theorem avoids ax-11 2162. (Contributed by Wolf Lammen, 26-Jun-2019.)
Assertion
Ref Expression
wl-nfae1 𝑥𝑦 𝑦 = 𝑥

Proof of Theorem wl-nfae1
StepHypRef Expression
1 aecom 2427 . 2 (∀𝑦 𝑦 = 𝑥 ↔ ∀𝑥 𝑥 = 𝑦)
2 nfa1 2156 . 2 𝑥𝑥 𝑥 = 𝑦
31, 2nfxfr 1859 1 𝑥𝑦 𝑦 = 𝑥
Colors of variables: wff setvar class
Syntax hints:  wal 1540  wnf 1790
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-10 2145  ax-12 2179  ax-13 2372
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-ex 1787  df-nf 1791
This theorem is referenced by:  wl-nfnae1  35310
  Copyright terms: Public domain W3C validator