Theorem reuxfr2 4676

Description: Transfer existential uniqueness from a variable to another variable contained in expression . (Contributed by NM, 14-Nov-2004.) (Revised by NM, 16-Jun-2017.)

Hypotheses

Ref	Expression
reuxfr2.1
reuxfr2.2

Assertion

Ref	Expression
reuxfr2

Distinct variable groups:   ,   ,   ,,

Proof of Theorem reuxfr2

Step	Hyp	Ref	Expression
1		reuxfr2.1	. . . 4
2	1	adantl 466	. . 3
3		reuxfr2.2	. . . 4
4	3	adantl 466	. . 3
5	2, 4	reuxfr2d 4675	. 2
6	5	trud 1404	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  wtru 1396  e.wcel 1818  E.wrex 2808  E!wreu 2809  E*wrmo 2810

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-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812  df-rex 2813  df-reu 2814  df-rmo 2815  df-v 3111