Theorem reu7 3294

Description: Restricted uniqueness using implicit substitution. (Contributed by NM, 24-Oct-2006.)

Hypothesis

Ref	Expression
rmo4.1

Assertion

Ref	Expression
reu7

Distinct variable groups:   ,,   ,   ,

Proof of Theorem reu7

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		reu3 3289	. 2
2		rmo4.1	. . . . . . 7
3		equequ1 1798	. . . . . . . 8
4		equcom 1794	. . . . . . . 8
5	3, 4	syl6bb 261	. . . . . . 7
6	2, 5	imbi12d 320	. . . . . 6
7	6	cbvralv 3084	. . . . 5
8	7	rexbii 2959	. . . 4
9		equequ1 1798	. . . . . . 7
10	9	imbi2d 316	. . . . . 6
11	10	ralbidv 2896	. . . . 5
12	11	cbvrexv 3085	. . . 4
13	8, 12	bitri 249	. . 3
14	13	anbi2i 694	. 2
15	1, 14	bitri 249	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wral 2807  E.wrex 2808  E!wreu 2809

This theorem is referenced by:  cshwrepswhash1  14587

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-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-reu 2814  df-rmo 2815