Theorem axc11nlem 1938

Description: Lemma for axc11n 2049. Change bound variable in an equality. (Contributed by NM, 8-Jul-2016.) (Proof shortened by Wolf Lammen, 17-Feb-2018.) Restructure to ease either bundling, or reducing dependencies on axioms. (Revised by Wolf Lammen, 30-Nov-2019.)

Hypothesis

Ref	Expression
axc11nlem.1

Assertion

Ref	Expression
axc11nlem

Distinct variable groups:   ,   ,

Proof of Theorem axc11nlem

Step	Hyp	Ref	Expression
1		cbvaev 1817	. . 3
2		equequ2 1799	. . . . 5
3	2	biimprd 223	. . . 4
4	3	al2imi 1636	. . 3
5	1, 4	syl5com 30	. 2
6		axc11nlem.1	. . . . 5
7	6	spsd 1867	. . . 4
8	7	com12 31	. . 3
9	8	con1d 124	. 2
10	5, 9	pm2.61d 158	1

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

This theorem is referenced by:  aevlem1  1939  axc11n  2049

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-12 1854

This theorem depends on definitions:  df-bi 185  df-ex 1613