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Theorem uneqri 3645
Description: Inference from membership to union. (Contributed by NM, 21-Jun-1993.)
Hypothesis
Ref Expression
uneqri.1
Assertion
Ref Expression
uneqri
Distinct variable groups:   ,   ,   ,

Proof of Theorem uneqri
StepHypRef Expression
1 elun 3644 . . 3
2 uneqri.1 . . 3
31, 2bitri 249 . 2
43eqriv 2453 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  \/wo 368  =wceq 1395  e.wcel 1818  u.cun 3473
This theorem is referenced by:  unidm  3646  uncom  3647  unass  3660  dfun2  3732  undi  3744  unab  3764  un0  3810  inundif  3906
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-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480
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