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Theorem tposoprab 6507
 Description: Transposition of a class of ordered triples. (Contributed by Mario Carneiro, 10-Sep-2015.)
Hypothesis
Ref Expression
tposoprab.1
Assertion
Ref Expression
tposoprab tpos
Distinct variable group:   ,,
Allowed substitution hints:   (,,)   (,,)

Proof of Theorem tposoprab
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 tposoprab.1 . . 3
21tposeqi 6504 . 2 tpos tpos
3 reldmoprab 6150 . . 3
4 dftpos3 6489 . . 3 tpos
53, 4ax-mp 8 . 2 tpos
6 nfcv 2571 . . . . 5
7 nfoprab2 6116 . . . . 5
8 nfcv 2571 . . . . 5
96, 7, 8nfbr 4248 . . . 4
10 nfcv 2571 . . . . 5
11 nfoprab1 6115 . . . . 5
12 nfcv 2571 . . . . 5
1310, 11, 12nfbr 4248 . . . 4
14 nfv 1629 . . . 4
15 nfv 1629 . . . 4
16 opeq12 3978 . . . . . 6
1716ancoms 440 . . . . 5
1817breq1d 4214 . . . 4
199, 13, 14, 15, 18cbvoprab12 6138 . . 3
20 nfcv 2571 . . . . 5
21 nfoprab3 6117 . . . . 5
22 nfcv 2571 . . . . 5
2320, 21, 22nfbr 4248 . . . 4
24 nfv 1629 . . . 4
25 breq2 4208 . . . . 5
26 df-br 4205 . . . . . 6
27 oprabid 6097 . . . . . 6
2826, 27bitri 241 . . . . 5
2925, 28syl6bb 253 . . . 4
3023, 24, 29cbvoprab3 6140 . . 3
3119, 30eqtri 2455 . 2
322, 5, 313eqtri 2459 1 tpos
 Colors of variables: wff set class Syntax hints:   wa 359   wceq 1652   wcel 1725  cop 3809   class class class wbr 4204   cdm 4870   wrel 4875  coprab 6074  tpos ctpos 6470 This theorem is referenced by:  tposmpt2  6508 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-pw 3793  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-ima 4883  df-iota 5410  df-fun 5448  df-fn 5449  df-fv 5454  df-oprab 6077  df-tpos 6471
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