Theorem cbvaldva 2032

Description: Rule used to change the bound variable in a universal quantifier with implicit substitution. Deduction form. (Contributed by David Moews, 1-May-2017.)

Hypothesis

Ref	Expression
cbvaldva.1

Assertion

Ref	Expression
cbvaldva

Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem cbvaldva

Step	Hyp	Ref	Expression
1		nfv 1707	. 2
2		nfvd 1708	. 2
3		cbvaldva.1	. . 3
4	3	ex 434	. 2
5	1, 2, 4	cbvald 2025	1

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

This theorem is referenced by:  cbvraldva2  3088

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