Theorem wl-nfae1

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

	Ref	Expression
Assertion	wl-nfae1	⊢ Ⅎ 𝑥 ∀ 𝑦 𝑦 = 𝑥

Proof

Step	Hyp	Ref	Expression
1		aecom	⊢ ( ∀ 𝑦 𝑦 = 𝑥 ↔ ∀ 𝑥 𝑥 = 𝑦 )
2		nfa1	⊢ Ⅎ 𝑥 ∀ 𝑥 𝑥 = 𝑦
3	1 2	nfxfr	⊢ Ⅎ 𝑥 ∀ 𝑦 𝑦 = 𝑥