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Theorem bnj1149 29919
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1149.1 (𝜑𝐴 ∈ V)
bnj1149.2 (𝜑𝐵 ∈ V)
Assertion
Ref Expression
bnj1149 (𝜑 → (𝐴𝐵) ∈ V)

Proof of Theorem bnj1149
StepHypRef Expression
1 bnj1149.1 . 2 (𝜑𝐴 ∈ V)
2 bnj1149.2 . 2 (𝜑𝐵 ∈ V)
3 unexg 6830 . 2 ((𝐴 ∈ V ∧ 𝐵 ∈ V) → (𝐴𝐵) ∈ V)
41, 2, 3syl2anc 690 1 (𝜑 → (𝐴𝐵) ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 1975  Vcvv 3168  cun 3533
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-8 1977  ax-9 1984  ax-10 2004  ax-11 2019  ax-12 2031  ax-13 2228  ax-ext 2585  ax-sep 4699  ax-nul 4708  ax-pr 4824  ax-un 6820
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1866  df-clab 2592  df-cleq 2598  df-clel 2601  df-nfc 2735  df-rex 2897  df-v 3170  df-dif 3538  df-un 3540  df-in 3542  df-ss 3549  df-nul 3870  df-sn 4121  df-pr 4123  df-uni 4363
This theorem is referenced by:  bnj1136  30121  bnj1413  30159  bnj1452  30176  bnj1489  30180
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