Theorem wl-ax11-lem4 33365

Description: Lemma. (Contributed by Wolf Lammen, 30-Jun-2019.)

Assertion

Ref	Expression
wl-ax11-lem4	|- F/ x ( A. u u = y /\ -. A. x x = y )

Distinct variable group:   x, u

Proof of Theorem wl-ax11-lem4

Step	Hyp	Ref	Expression
1		ancom 466	. 2 |- ( ( A. u u = y /\ -. A. x x = y ) <-> ( -. A. x x = y /\ A. u u = y ) )
2		nfna1 2029	. . 3 |- F/ x -. A. x x = y
3		wl-ax11-lem3 33364	. . 3 |- ( -. A. x x = y -> F/ x A. u u = y )
4	2, 3	nfan1 2068	. 2 |- F/ x ( -. A. x x = y /\ A. u u = y )
5	1, 4	nfxfr 1779	1 |- F/ x ( A. u u = y /\ -. A. x x = y )

Syntax hints:   -. wn 3   /\ wa 384   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  ax-wl-11v 33361

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710

This theorem is referenced by:  wl-ax11-lem8  33369