Theorem wl-nfae1 31818

Description: Unlike nfae 2112, this specialized theorem avoids ax-11 1893. (Contributed by Wolf Lammen, 26-Jun-2019.)

Assertion

Ref	Expression
wl-nfae1	|- F/ x A. y y = x

Proof of Theorem wl-nfae1

Step	Hyp	Ref	Expression
1		aecom 2107	. 2 |- ( A. y y = x <-> A. x x = y )
2		nfa1 1953	. 2 |- F/ x A. x x = y
3	1, 2	nfxfr 1693	1 |- F/ x A. y y = x

Syntax hints:   A.wal 1436   F/wnf 1664

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-12 1906  ax-13 2054

This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1661  df-nf 1665

This theorem is referenced by:  wl-nfnae1  31819