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Theorem eusvobj1 6576
 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:   ,,   ,
Allowed substitution hint:   ()

Proof of Theorem eusvobj1
StepHypRef Expression
1 nfeu1 2291 . . 3
2 eusvobj1.1 . . . 4
32eusvobj2 6575 . . 3
41, 3alrimi 1781 . 2
5 iotabi 5420 . 2
64, 5syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549   wceq 1652   wcel 1725  weu 2281  wral 2698  wrex 2699  cvv 2949  cio 5409 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2703  df-rex 2704  df-v 2951  df-sbc 3155  df-csb 3245  df-dif 3316  df-nul 3622  df-sn 3813  df-uni 4009  df-iota 5411
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