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Theorem bnj1149 31170
 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 7124 . 2 ((𝐴 ∈ V ∧ 𝐵 ∈ V) → (𝐴𝐵) ∈ V)
41, 2, 3syl2anc 696 1 (𝜑 → (𝐴𝐵) ∈ V)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2139  Vcvv 3340   ∪ cun 3713 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-8 2141  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740  ax-sep 4933  ax-nul 4941  ax-pr 5055  ax-un 7114 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-rex 3056  df-v 3342  df-dif 3718  df-un 3720  df-in 3722  df-ss 3729  df-nul 4059  df-sn 4322  df-pr 4324  df-uni 4589 This theorem is referenced by:  bnj1136  31372  bnj1413  31410  bnj1452  31427  bnj1489  31431
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