Theorem wl-nfae1 38035

Description: Unlike nfae 2466, this specialized theorem avoids ax-11 2193. (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 2460	. 2 ⊢ (∀𝑦 𝑦 = 𝑥 ↔ ∀𝑥 𝑥 = 𝑦)
2		nfa1 2187	. 2 ⊢ Ⅎ𝑥∀𝑥 𝑥 = 𝑦
3	1, 2	nfxfr 1875	1 ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥

Syntax hints:  ∀wal 1560  Ⅎwnf 1805

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-5 1932  ax-6 1989  ax-7 2030  ax-10 2177  ax-12 2214  ax-13 2405

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-ex 1802  df-nf 1806

This theorem is referenced by:  wl-nfnae1  38036