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Theorem dfmpt2 6437
 Description: Alternate definition for the "maps to" notation df-mpt2 6086 (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:   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem dfmpt2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 mpt2mpts 6415 . 2
2 fvex 5742 . . . 4
3 fvex 5742 . . . . 5
4 dfmpt2.1 . . . . 5
53, 4csbex 3262 . . . 4
62, 5csbex 3262 . . 3
76dfmpt 5911 . 2
8 nfcv 2572 . . . . 5
9 nfcsb1v 3283 . . . . 5
108, 9nfop 4000 . . . 4
1110nfsn 3866 . . 3
12 nfcv 2572 . . . . 5
13 nfcv 2572 . . . . . 6
14 nfcsb1v 3283 . . . . . 6
1513, 14nfcsb 3285 . . . . 5
1612, 15nfop 4000 . . . 4
1716nfsn 3866 . . 3
18 nfcv 2572 . . 3
19 id 20 . . . . 5
20 csbopeq1a 6400 . . . . 5
2119, 20opeq12d 3992 . . . 4
2221sneqd 3827 . . 3
2311, 17, 18, 22iunxpf 5021 . 2
241, 7, 233eqtri 2460 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   wcel 1725  cvv 2956  csb 3251  csn 3814  cop 3817  ciun 4093   cmpt 4266   cxp 4876  cfv 5454   cmpt2 6083  c1st 6347  c2nd 6348 This theorem is referenced by:  fpar  6450 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 2417  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403  ax-un 4701 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-reu 2712  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  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-uni 4016  df-iun 4095  df-br 4213  df-opab 4267  df-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-iota 5418  df-fun 5456  df-fn 5457  df-f 5458  df-f1 5459  df-fo 5460  df-f1o 5461  df-fv 5462  df-oprab 6085  df-mpt2 6086  df-1st 6349  df-2nd 6350
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