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Theorem bnj519 29080
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 5314 . 2  |-  ( ( A  e.  _V  /\  B  e.  _V )  ->  Fun  { <. A ,  B >. } )
31, 2mpan 651 1  |-  ( B  e.  _V  ->  Fun  {
<. A ,  B >. } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1696   _Vcvv 2801   {csn 3653   <.cop 3656   Fun wfun 5265
This theorem is referenced by:  bnj97  29214  bnj535  29238
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-eu 2160  df-mo 2161  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-br 4040  df-opab 4094  df-id 4325  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-fun 5273
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