Theorem eusvobj1 6290

Description: Specify the same object in two ways when class () is single-valued. (Contributed by NM, 1-Nov-2010.) (Proof shortened by Mario Carneiro, 19-Nov-2016.)

Hypothesis

Ref	Expression
eusvobj1.1

Assertion

Ref	Expression
eusvobj1

Distinct variable groups:   ,,   ,

Proof of Theorem eusvobj1

Step	Hyp	Ref	Expression
1		nfeu1 2294	. . 3
2		eusvobj1.1	. . . 4
3	2	eusvobj2 6289	. . 3
4	1, 3	alrimi 1877	. 2
5		iotabi 5565	. 2
6	4, 5	syl 16	1

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  =wceq 1395  e.wcel 1818  E!weu 2282  A.wral 2807  E.wrex 2808  cvv 3109  iotacio 5554

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-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-nul 3785  df-sn 4030  df-uni 4250  df-iota 5556