Theorem cbv3 2015

Description: Rule used to change bound variables, using implicit substitution, that does not use ax-c9 2221. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 12-May-2018.)

Hypotheses

Ref	Expression
cbv3.1
cbv3.2
cbv3.3

Assertion

Ref	Expression
cbv3

Proof of Theorem cbv3

Step	Hyp	Ref	Expression
1		cbv3.1	. . 3
2	1	nfal 1947	. 2
3		cbv3.2	. . 3
4		cbv3.3	. . 3
5	3, 4	spim 2006	. 2
6	2, 5	alrimi 1877	1

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

This theorem is referenced by:  cbv3h  2016  cbv1  2017  cbval  2021  axc16i  2064  mo3OLD  2324

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