Theorem ralxfr 4670

Description: Transfer universal quantification from a variable to another variable contained in expression . (Contributed by NM, 10-Jun-2005.) (Revised by Mario Carneiro, 15-Aug-2014.)

Hypotheses

Ref	Expression
ralxfr.1
ralxfr.2
ralxfr.3

Assertion

Ref	Expression
ralxfr

Distinct variable groups:   ,   ,   ,   ,,   ,

Proof of Theorem ralxfr

Step	Hyp	Ref	Expression
1		ralxfr.1	. . . 4
2	1	adantl 466	. . 3
3		ralxfr.2	. . . 4
4	3	adantl 466	. . 3
5		ralxfr.3	. . . 4
6	5	adantl 466	. . 3
7	2, 4, 6	ralxfrd 4666	. 2
8	7	trud 1404	1

Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  wtru 1396  e.wcel 1818  A.wral 2807  E.wrex 2808

This theorem is referenced by:  rexxfr  4672  infm3  10527

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-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-v 3111