Theorem reuxfr2d 4675

Description: Transfer existential uniqueness from a variable to another variable contained in expression . (Contributed by NM, 16-Jan-2012.) (Revised by NM, 16-Jun-2017.)

Hypotheses

Ref	Expression
reuxfr2d.1
reuxfr2d.2

Assertion

Ref	Expression
reuxfr2d

Distinct variable groups:   ,,   ,   ,   ,,

Proof of Theorem reuxfr2d

Step	Hyp	Ref	Expression
1		reuxfr2d.2	. . . . . . 7
2		rmoan 3298	. . . . . . 7
3	1, 2	syl 16	. . . . . 6
4		ancom 450	. . . . . . 7
5	4	rmobii 3049	. . . . . 6
6	3, 5	sylib 196	. . . . 5
7	6	ralrimiva 2871	. . . 4
8		2reuswap 3302	. . . 4
9	7, 8	syl 16	. . 3
10		df-rmo 2815	. . . . . 6
11	10	ralbii 2888	. . . . 5
12		2reuswap 3302	. . . . 5
13	11, 12	sylbir 213	. . . 4
14		moeq 3275	. . . . . . 7
15	14	moani 2346	. . . . . 6
16		ancom 450	. . . . . . . 8
17		an12 797	. . . . . . . 8
18	16, 17	bitri 249	. . . . . . 7
19	18	mobii 2307	. . . . . 6
20	15, 19	mpbi 208	. . . . 5
21	20	a1i 11	. . . 4
22	13, 21	mprg 2820	. . 3
23	9, 22	impbid1 203	. 2
24		reuxfr2d.1	. . . 4
25		biidd 237	. . . . 5
26	25	ceqsrexv 3233	. . . 4
27	24, 26	syl 16	. . 3
28	27	reubidva 3041	. 2
29	23, 28	bitrd 253	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  E*wmo 2283  A.wral 2807  E.wrex 2808  E!wreu 2809  E*wrmo 2810

This theorem is referenced by:  reuxfr2  4676  reuxfrd  4677

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