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Theorem txpss3v 25723
 Description: A tail cross product is a subset of the class of ordered triples. (Contributed by Scott Fenton, 31-Mar-2012.)
Assertion
Ref Expression
txpss3v

Proof of Theorem txpss3v
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-txp 25698 . 2
2 inss1 3561 . . 3
3 relco 5368 . . . 4
4 vex 2959 . . . . . . . . 9
5 vex 2959 . . . . . . . . 9
64, 5brcnv 5055 . . . . . . . 8
74brres 5152 . . . . . . . . 9
87simprbi 451 . . . . . . . 8
96, 8sylbi 188 . . . . . . 7
109adantl 453 . . . . . 6
1110exlimiv 1644 . . . . 5
12 vex 2959 . . . . . 6
1312, 5opelco 5044 . . . . 5
14 opelxp 4908 . . . . . 6
1512, 14mpbiran 885 . . . . 5
1611, 13, 153imtr4i 258 . . . 4
173, 16relssi 4967 . . 3
182, 17sstri 3357 . 2
191, 18eqsstri 3378 1
 Colors of variables: wff set class Syntax hints:   wa 359  wex 1550   wcel 1725  cvv 2956   cin 3319   wss 3320  cop 3817   class class class wbr 4212   cxp 4876  ccnv 4877   cres 4880   ccom 4882  c1st 6347  c2nd 6348   ctxp 25674 This theorem is referenced by:  txprel  25724  brtxp2  25726  pprodss4v  25729 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-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-res 4890  df-txp 25698
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