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Theorem bnj1149 34785
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 7762 . 2 ((𝐴 ∈ V ∧ 𝐵 ∈ V) → (𝐴𝐵) ∈ V)
41, 2, 3syl2anc 584 1 (𝜑 → (𝐴𝐵) ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  Vcvv 3478  cun 3961
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-sep 5302  ax-nul 5312  ax-pr 5438  ax-un 7754
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-sn 4632  df-pr 4634  df-uni 4913
This theorem is referenced by:  bnj1136  34990  bnj1413  35028  bnj1452  35045  bnj1489  35049
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