Theorem cbval2 2027

Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 22-Dec-2003.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 22-Apr-2018.)

Hypotheses

Ref	Expression
cbval2.1
cbval2.2
cbval2.3
cbval2.4
cbval2.5

Assertion

Ref	Expression
cbval2

Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem cbval2

Step	Hyp	Ref	Expression
1		cbval2.1	. . 3
2	1	nfal 1947	. 2
3		cbval2.3	. . 3
4	3	nfal 1947	. 2
5		nfv 1707	. . . . . 6
6		cbval2.2	. . . . . 6
7	5, 6	nfim 1920	. . . . 5
8		nfv 1707	. . . . . 6
9		cbval2.4	. . . . . 6
10	8, 9	nfim 1920	. . . . 5
11		cbval2.5	. . . . . . 7
12	11	expcom 435	. . . . . 6
13	12	pm5.74d 247	. . . . 5
14	7, 10, 13	cbval 2021	. . . 4
15		19.21v 1729	. . . 4
16		19.21v 1729	. . . 4
17	14, 15, 16	3bitr3i 275	. . 3
18	17	pm5.74ri 246	. 2
19	2, 4, 18	cbval 2021	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  F/wnf 1616

This theorem is referenced by:  cbvex2  2028  cbval2v  2030  2eu6OLD  2384

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