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Theorem txprel 34396
Description: A tail Cartesian product is a relationship. (Contributed by Scott Fenton, 31-Mar-2012.)
Assertion
Ref Expression
txprel Rel (𝐴𝐵)

Proof of Theorem txprel
StepHypRef Expression
1 txpss3v 34395 . . 3 (𝐴𝐵) ⊆ (V × (V × V))
2 xpss 5647 . . 3 (V × (V × V)) ⊆ (V × V)
31, 2sstri 3951 . 2 (𝐴𝐵) ⊆ (V × V)
4 df-rel 5638 . 2 (Rel (𝐴𝐵) ↔ (𝐴𝐵) ⊆ (V × V))
53, 4mpbir 230 1 Rel (𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3443  wss 3908   × cxp 5629  Rel wrel 5636  ctxp 34347
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707  ax-sep 5254  ax-nul 5261  ax-pr 5382
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-ral 3063  df-rex 3072  df-rab 3406  df-v 3445  df-dif 3911  df-un 3913  df-in 3915  df-ss 3925  df-nul 4281  df-if 4485  df-sn 4585  df-pr 4587  df-op 4591  df-br 5104  df-opab 5166  df-xp 5637  df-rel 5638  df-cnv 5639  df-co 5640  df-res 5643  df-txp 34371
This theorem is referenced by:  pprodss4v  34401
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