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Theorem bnj519 29103
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Revised by Mario Carneiro, 6-May-2015.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj519.1  |-  A  e. 
_V
Assertion
Ref Expression
bnj519  |-  ( B  e.  _V  ->  Fun  {
<. A ,  B >. } )

Proof of Theorem bnj519
StepHypRef Expression
1 bnj519.1 . 2  |-  A  e. 
_V
2 funsng 5497 . 2  |-  ( ( A  e.  _V  /\  B  e.  _V )  ->  Fun  { <. A ,  B >. } )
31, 2mpan 652 1  |-  ( B  e.  _V  ->  Fun  {
<. A ,  B >. } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   _Vcvv 2956   {csn 3814   <.cop 3817   Fun wfun 5448
This theorem is referenced by:  bnj97  29237  bnj535  29261
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-fun 5456
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