Metamath Proof Explorer


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