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Theorem brtxp2 25718
 Description: The binary relationship over a tail cross when the second argument is not an ordered pair. (Contributed by Scott Fenton, 14-Apr-2014.) (Revised by Mario Carneiro, 3-May-2015.)
Hypothesis
Ref Expression
brtxp2.1
Assertion
Ref Expression
brtxp2
Distinct variable groups:   ,,   ,,   ,,   ,,

Proof of Theorem brtxp2
StepHypRef Expression
1 txpss3v 25715 . . . . . . 7
21brel 4918 . . . . . 6
32simprd 450 . . . . 5
4 elvv 4928 . . . . 5
53, 4sylib 189 . . . 4
65pm4.71ri 615 . . 3
7 19.41vv 1925 . . 3
86, 7bitr4i 244 . 2
9 breq2 4208 . . . 4
109pm5.32i 619 . . 3
11102exbii 1593 . 2
12 brtxp2.1 . . . . . 6
13 vex 2951 . . . . . 6
14 vex 2951 . . . . . 6
1512, 13, 14brtxp 25717 . . . . 5
1615anbi2i 676 . . . 4
17 3anass 940 . . . 4
1816, 17bitr4i 244 . . 3
19182exbii 1593 . 2
208, 11, 193bitri 263 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   w3a 936  wex 1550   wceq 1652   wcel 1725  cvv 2948  cop 3809   class class class wbr 4204   cxp 4868   ctxp 25666 This theorem is referenced by:  brsuccf  25778  brrestrict  25786 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-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pow 4369  ax-pr 4395  ax-un 4693 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 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-res 4882  df-iota 5410  df-fun 5448  df-fn 5449  df-f 5450  df-fo 5452  df-fv 5454  df-1st 6341  df-2nd 6342  df-txp 25690
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