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Theorem bj-xpexg2 33251
Description: Curried (exported) form of xpexg 7123. (Contributed by BJ, 2-Apr-2019.)
Assertion
Ref Expression
bj-xpexg2 (𝐴𝑉 → (𝐵𝑊 → (𝐴 × 𝐵) ∈ V))

Proof of Theorem bj-xpexg2
StepHypRef Expression
1 xpexg 7123 . 2 ((𝐴𝑉𝐵𝑊) → (𝐴 × 𝐵) ∈ V)
21ex 449 1 (𝐴𝑉 → (𝐵𝑊 → (𝐴 × 𝐵) ∈ V))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2137  Vcvv 3338   × cxp 5262
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1986  ax-6 2052  ax-7 2088  ax-8 2139  ax-9 2146  ax-10 2166  ax-11 2181  ax-12 2194  ax-13 2389  ax-ext 2738  ax-sep 4931  ax-nul 4939  ax-pow 4990  ax-pr 5053  ax-un 7112
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2045  df-clab 2745  df-cleq 2751  df-clel 2754  df-nfc 2889  df-ral 3053  df-rex 3054  df-rab 3057  df-v 3340  df-dif 3716  df-un 3718  df-in 3720  df-ss 3727  df-nul 4057  df-if 4229  df-pw 4302  df-sn 4320  df-pr 4322  df-op 4326  df-uni 4587  df-opab 4863  df-xp 5270  df-rel 5271
This theorem is referenced by:  bj-xpnzexb  33252  bj-xtagex  33281
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