Theorem wl-nfae1 35686

Description: Unlike nfae 2433, this specialized theorem avoids ax-11 2154. (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 2427	. 2 ⊢ (∀𝑦 𝑦 = 𝑥 ↔ ∀𝑥 𝑥 = 𝑦)
2		nfa1 2148	. 2 ⊢ Ⅎ𝑥∀𝑥 𝑥 = 𝑦
3	1, 2	nfxfr 1855	1 ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥

Syntax hints:  ∀wal 1537  Ⅎwnf 1786

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-10 2137  ax-12 2171  ax-13 2372

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-ex 1783  df-nf 1787

This theorem is referenced by:  wl-nfnae1  35687