Theorem wl-nfae1 33315

Description: Unlike nfae 2316, this specialized theorem avoids ax-11 2034. (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 2311	. 2 |- ( A. y y = x <-> A. x x = y )
2		nfa1 2028	. 2 |- F/ x A. x x = y
3	1, 2	nfxfr 1779	1 |- F/ x A. y y = x

Syntax hints:   A.wal 1481   F/wnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710

This theorem is referenced by:  wl-nfnae1  33316