Theorem axc9lem2 2040

Description: Lemma for nfeqf2 2041. This lemma is equivalent to ax13v 2000 with one distinct variable constraint removed. (Contributed by Wolf Lammen, 8-Sep-2018.) (New usage is discouraged.)

Assertion

Ref	Expression
axc9lem2

Distinct variable group:   ,

Proof of Theorem axc9lem2

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		axc9lem1 2001	. . . 4
2		equequ2 1799	. . . . . . 7
3	2	biimprcd 225	. . . . . 6
4	3	eximi 1656	. . . . 5
5		19.36v 1762	. . . . 5
6	4, 5	sylib 196	. . . 4
7	1, 6	syl9 71	. . 3
8	7	alrimdv 1721	. 2
9		nfv 1707	. . 3
10	9, 2	equsal 2036	. 2
11	8, 10	syl6ib 226	1

Syntax hints:  -.wn 3  ->wi 4  A.wal 1393  E.wex 1612

This theorem is referenced by:  nfeqf2  2041

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617