Theorem reuxfrd 4677

Description: Transfer existential uniqueness from a variable to another variable contained in expression . Use reuhypd 4679 to eliminate the second hypothesis. (Contributed by NM, 16-Jan-2012.)

Hypotheses

Ref	Expression
reuxfrd.1
reuxfrd.2
reuxfrd.3

Assertion

Ref	Expression
reuxfrd

Distinct variable groups:   ,,   ,   ,   ,   ,,

Proof of Theorem reuxfrd

Step	Hyp	Ref	Expression
1		reuxfrd.2	. . . . . 6
2		reurex 3074	. . . . . 6
3	1, 2	syl 16	. . . . 5
4	3	biantrurd 508	. . . 4
5		r19.41v 3009	. . . . 5
6		reuxfrd.3	. . . . . . 7
7	6	pm5.32i 637	. . . . . 6
8	7	rexbii 2959	. . . . 5
9	5, 8	bitr3i 251	. . . 4
10	4, 9	syl6bb 261	. . 3
11	10	reubidva 3041	. 2
12		reuxfrd.1	. . 3
13		reurmo 3075	. . . 4
14	1, 13	syl 16	. . 3
15	12, 14	reuxfr2d 4675	. 2
16	11, 15	bitrd 253	1

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

This theorem is referenced by:  reuxfr  4678  riotaxfrd  6288

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