Theorem reueq1f 3052

Description: Equality theorem for restricted uniqueness quantifier, with bound-variable hypotheses instead of distinct variable restrictions. (Contributed by NM, 5-Apr-2004.) (Revised by Andrew Salmon, 11-Jul-2011.)

Hypotheses

Ref	Expression
raleq1f.1
raleq1f.2

Assertion

Ref	Expression
reueq1f

Proof of Theorem reueq1f

Step	Hyp	Ref	Expression
1		raleq1f.1	. . . 4
2		raleq1f.2	. . . 4
3	1, 2	nfeq 2630	. . 3
4		eleq2 2530	. . . 4
5	4	anbi1d 704	. . 3
6	3, 5	eubid 2302	. 2
7		df-reu 2814	. 2
8		df-reu 2814	. 2
9	6, 7, 8	3bitr4g 288	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  E!weu 2282  F/_wnfc 2605  E!wreu 2809

This theorem is referenced by:  reueq1  3056

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-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-eu 2286  df-cleq 2449  df-clel 2452  df-nfc 2607  df-reu 2814