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Theorem opelvv 5724
Description: Ordered pair membership in the universal class of ordered pairs. (Contributed by NM, 22-Aug-2013.) (Revised by Mario Carneiro, 26-Apr-2015.)
Hypotheses
Ref Expression
opelvv.1 𝐴 ∈ V
opelvv.2 𝐵 ∈ V
Assertion
Ref Expression
opelvv 𝐴, 𝐵⟩ ∈ (V × V)

Proof of Theorem opelvv
StepHypRef Expression
1 opelvv.1 . 2 𝐴 ∈ V
2 opelvv.2 . 2 𝐵 ∈ V
3 opelxpi 5721 . 2 ((𝐴 ∈ V ∧ 𝐵 ∈ V) → ⟨𝐴, 𝐵⟩ ∈ (V × V))
41, 2, 3mp2an 692 1 𝐴, 𝐵⟩ ∈ (V × V)
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  Vcvv 3479  cop 4631   × cxp 5682
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707  ax-sep 5295  ax-nul 5305  ax-pr 5431
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-ral 3061  df-rex 3070  df-rab 3436  df-v 3481  df-dif 3953  df-un 3955  df-ss 3967  df-nul 4333  df-if 4525  df-sn 4626  df-pr 4628  df-op 4632  df-opab 5205  df-xp 5690
This theorem is referenced by:  relopabiALT  5832  funsneqopb  7171  isof1oopb  7346  1st2ndb  8055  eqop2  8058  evlfcl  18268  brtxp  35882  brpprod  35887  brsset  35891  brcart  35934  brcup  35941  brcap  35942  elcnvlem  43619  swapfelvv  48987  fucoelvv  49038
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