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Theorem txprel 25725
Description: A tail cross product is a relationship. (Contributed by Scott Fenton, 31-Mar-2012.)
Assertion
Ref Expression
txprel  |-  Rel  ( A  (x)  B )

Proof of Theorem txprel
StepHypRef Expression
1 txpss3v 25724 . . 3  |-  ( A 
(x)  B )  C_  ( _V  X.  ( _V  X.  _V ) )
2 xpss 4983 . . 3  |-  ( _V 
X.  ( _V  X.  _V ) )  C_  ( _V  X.  _V )
31, 2sstri 3358 . 2  |-  ( A 
(x)  B )  C_  ( _V  X.  _V )
4 df-rel 4886 . 2  |-  ( Rel  ( A  (x)  B
)  <->  ( A  (x)  B )  C_  ( _V  X.  _V ) )
53, 4mpbir 202 1  |-  Rel  ( A  (x)  B )
Colors of variables: wff set class
Syntax hints:   _Vcvv 2957    C_ wss 3321    X. cxp 4877   Rel wrel 4884    (x) ctxp 25675
This theorem is referenced by:  pprodss4v  25730
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2286  df-mo 2287  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-br 4214  df-opab 4268  df-xp 4885  df-rel 4886  df-cnv 4887  df-co 4888  df-res 4891  df-txp 25699
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