Theorem wl-nfae1 34771

Description: Unlike nfae 2454, this specialized theorem avoids ax-11 2160. (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 2448	. 2 ⊢ (∀𝑦 𝑦 = 𝑥 ↔ ∀𝑥 𝑥 = 𝑦)
2		nfa1 2154	. 2 ⊢ Ⅎ𝑥∀𝑥 𝑥 = 𝑦
3	1, 2	nfxfr 1852	1 ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥

Syntax hints:  ∀wal 1534  Ⅎwnf 1783

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-10 2144  ax-12 2176  ax-13 2389

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-ex 1780  df-nf 1784

This theorem is referenced by:  wl-nfnae1  34772