Theorem cbv2h 2019

Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 11-May-1993.)

Hypotheses

Ref	Expression
cbv2h.1
cbv2h.2
cbv2h.3

Assertion

Ref	Expression
cbv2h

Proof of Theorem cbv2h

Step	Hyp	Ref	Expression
1		cbv2h.1	. . 3
2		cbv2h.2	. . 3
3		cbv2h.3	. . . 4
4		bi1 186	. . . 4
5	3, 4	syl6 33	. . 3
6	1, 2, 5	cbv1h 2018	. 2
7		equcomi 1793	. . . . 5
8		bi2 198	. . . . 5
9	7, 3, 8	syl56 34	. . . 4
10	2, 1, 9	cbv1h 2018	. . 3
11	10	alcoms 1843	. 2
12	6, 11	impbid 191	1

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393

This theorem is referenced by:  cbv2  2020  eujustALT  2285

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