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Theorem unieqd 3902
 Description: Deduction of equality of two class unions. (Contributed by NM, 21-Apr-1995.)
Hypothesis
Ref Expression
unieqd.1 (φA = B)
Assertion
Ref Expression
unieqd (φA = B)

Proof of Theorem unieqd
StepHypRef Expression
1 unieqd.1 . 2 (φA = B)
2 unieq 3900 . 2 (A = BA = B)
31, 2syl 15 1 (φA = B)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642  ∪cuni 3891 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-uni 3892 This theorem is referenced by:  uniprg  3906  unisng  3908  iotaeq  4347  iotabi  4348  uniabio  4349  iotanul  4354  dfiota4  4372  elxp4  5108  funfv  5375  fvun  5378  fvco2  5382  fniunfv  5466
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