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Theorem dfmpt2 6890
Description: Alternate definition for the "maps to" notation df-mpt2 6301 (although it requires that be a set). (Contributed by NM, 19-Dec-2008.) (Revised by Mario Carneiro, 31-Aug-2015.)
Hypothesis
Ref Expression
dfmpt2.1
Assertion
Ref Expression
dfmpt2
Distinct variable groups:   , ,   , ,

Proof of Theorem dfmpt2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 mpt2mpts 6864 . 2
2 dfmpt2.1 . . . . 5
32csbex 4585 . . . 4
43csbex 4585 . . 3
54dfmpt 6076 . 2
6 nfcv 2619 . . . . 5
7 nfcsb1v 3450 . . . . 5
86, 7nfop 4233 . . . 4
98nfsn 4087 . . 3
10 nfcv 2619 . . . . 5
11 nfcv 2619 . . . . . 6
12 nfcsb1v 3450 . . . . . 6
1311, 12nfcsb 3452 . . . . 5
1410, 13nfop 4233 . . . 4
1514nfsn 4087 . . 3
16 nfcv 2619 . . 3
17 id 22 . . . . 5
18 csbopeq1a 6853 . . . . 5
1917, 18opeq12d 4225 . . . 4
2019sneqd 4041 . . 3
219, 15, 16, 20iunxpf 5156 . 2
221, 5, 213eqtri 2490 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  e.wcel 1818   cvv 3109  [_csb 3434  {csn 4029  <.cop 4035  U_ciun 4330  e.cmpt 4510  X.cxp 5002  `cfv 5593  e.cmpt2 6298   c1st 6798   c2nd 6799
This theorem is referenced by:  fpar  6904
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pow 4630  ax-pr 4691  ax-un 6592
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-fal 1401  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-reu 2814  df-rab 2816  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-iun 4332  df-br 4453  df-opab 4511  df-mpt 4512  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-iota 5556  df-fun 5595  df-fn 5596  df-f 5597  df-f1 5598  df-fo 5599  df-f1o 5600  df-fv 5601  df-oprab 6300  df-mpt2 6301  df-1st 6800  df-2nd 6801
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