Theorem euxfr2 3284

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

Hypotheses

Ref	Expression
euxfr2.1
euxfr2.2

Assertion

Ref	Expression
euxfr2

Distinct variable groups:   ,   ,

Proof of Theorem euxfr2

Step	Hyp	Ref	Expression
1		2euswap 2370	. . . 4
2		euxfr2.2	. . . . . 6
3	2	moani 2346	. . . . 5
4		ancom 450	. . . . . 6
5	4	mobii 2307	. . . . 5
6	3, 5	mpbi 208	. . . 4
7	1, 6	mpg 1620	. . 3
8		2euswap 2370	. . . 4
9		moeq 3275	. . . . . 6
10	9	moani 2346	. . . . 5
11	4	mobii 2307	. . . . 5
12	10, 11	mpbi 208	. . . 4
13	8, 12	mpg 1620	. . 3
14	7, 13	impbii 188	. 2
15		euxfr2.1	. . . 4
16		biidd 237	. . . 4
17	15, 16	ceqsexv 3146	. . 3
18	17	eubii 2306	. 2
19	14, 18	bitri 249	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  E!weu 2282  E*wmo 2283  cvv 3109

This theorem is referenced by:  euxfr  3285  euop2  4752

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-v 3111