Theorem cbvrexv2 3471

Description: Rule used to change the bound variable in a restricted existential quantifier with implicit substitution which also changes the quantifier domain. (Contributed by David Moews, 1-May-2017.)

Hypotheses

Ref	Expression
cbvralv2.1
cbvralv2.2

Assertion

Ref	Expression
cbvrexv2

Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem cbvrexv2

Step	Hyp	Ref	Expression
1		nfcv 2619	. 2
2		nfcv 2619	. 2
3		nfv 1707	. 2
4		nfv 1707	. 2
5		cbvralv2.2	. 2
6		cbvralv2.1	. 2
7	1, 2, 3, 4, 5, 6	cbvrexcsf 3467	1

Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  E.wrex 2808

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  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-sbc 3328  df-csb 3435