Theorem wl-nfae1 32494

Description: Unlike nfae 2304, this specialized theorem avoids ax-11 2021. (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 2299	. 2 ⊢ (∀𝑦 𝑦 = 𝑥 ↔ ∀𝑥 𝑥 = 𝑦)
2		nfa1 2015	. 2 ⊢ Ⅎ𝑥∀𝑥 𝑥 = 𝑦
3	1, 2	nfxfr 1771	1 ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥

Syntax hints:  ∀wal 1473  Ⅎwnf 1699

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034  ax-13 2234

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701

This theorem is referenced by:  wl-nfnae1  32495