Theorem wl-nfae1 37222

Description: Unlike nfae 2427, this specialized theorem avoids ax-11 2147. (Contributed by Wolf Lammen, 26-Jun-2019.)

Assertion

Ref	Expression
wl-nfae1	⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥

Proof of Theorem wl-nfae1

Step	Hyp	Ref	Expression
1		aecom 2421	. 2 ⊢ (∀𝑦 𝑦 = 𝑥 ↔ ∀𝑥 𝑥 = 𝑦)
2		nfa1 2141	. 2 ⊢ Ⅎ𝑥∀𝑥 𝑥 = 𝑦
3	1, 2	nfxfr 1848	1 ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥

Syntax hints:  ∀wal 1532  Ⅎwnf 1778

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-10 2130  ax-12 2167  ax-13 2366

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-ex 1775  df-nf 1779

This theorem is referenced by:  wl-nfnae1  37223