Theorem cbv2 2020

Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.) Format hypotheses to common style. (Revised by Wolf Lammen, 13-May-2018.)

Hypotheses

Ref	Expression
cbv2.1
cbv2.2
cbv2.3
cbv2.4
cbv2.5

Assertion

Ref	Expression
cbv2

Proof of Theorem cbv2

Step	Hyp	Ref	Expression
1		cbv2.1	. . 3
2		cbv2.2	. . . 4
3	2	nfri 1874	. . 3
4	1, 3	alrimi 1877	. 2
5		cbv2.3	. . . 4
6	5	nfrd 1875	. . 3
7		cbv2.4	. . . 4
8	7	nfrd 1875	. . 3
9		cbv2.5	. . 3
10	6, 8, 9	cbv2h 2019	. 2
11	4, 10	syl 16	1

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  F/wnf 1616

This theorem is referenced by:  cbvald  2025  sb9  2169  wl-cbvalnaed  29985  wl-sb8t  30000

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-11 1842  ax-12 1854  ax-13 1999

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