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Theorem opelvv 4751
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  e. 
_V
opelvv.2  |-  B  e. 
_V
Assertion
Ref Expression
opelvv  |-  <. A ,  B >.  e.  ( _V 
X.  _V )

Proof of Theorem opelvv
StepHypRef Expression
1 opelvv.1 . 2  |-  A  e. 
_V
2 opelvv.2 . 2  |-  B  e. 
_V
3 opelxpi 4737 . 2  |-  ( ( A  e.  _V  /\  B  e.  _V )  -> 
<. A ,  B >.  e.  ( _V  X.  _V ) )
41, 2, 3mp2an 653 1  |-  <. A ,  B >.  e.  ( _V 
X.  _V )
Colors of variables: wff set class
Syntax hints:    e. wcel 1696   _Vcvv 2801   <.cop 3656    X. cxp 4703
This theorem is referenced by:  relsnop  4807  relopabi  4827  1st2ndb  6176  eqop2  6179  evlfcl  14012  brtxp  24491  brpprod  24496  brsset  24500  brcart  24542  brcup  24549  brcap  24550  stcat  25147  eloi  25189
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-opab 4094  df-xp 4711
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