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Theorem dfmpt2 6897
 Description: Alternate definition for the "maps to" notation df-mpt2 6310 (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 6871 . 2
2 dfmpt2.1 . . . . 5
32csbex 4559 . . . 4
43csbex 4559 . . 3
54dfmpt 6084 . 2
6 nfcv 2580 . . . . 5
7 nfcsb1v 3411 . . . . 5
86, 7nfop 4203 . . . 4
98nfsn 4057 . . 3
10 nfcv 2580 . . . . 5
11 nfcv 2580 . . . . . 6
12 nfcsb1v 3411 . . . . . 6
1311, 12nfcsb 3413 . . . . 5
1410, 13nfop 4203 . . . 4
1514nfsn 4057 . . 3
16 nfcv 2580 . . 3
17 id 22 . . . . 5
18 csbopeq1a 6860 . . . . 5
1917, 18opeq12d 4195 . . . 4
2019sneqd 4010 . . 3
219, 15, 16, 20iunxpf 5002 . 2
221, 5, 213eqtri 2455 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1437   wcel 1872  cvv 3080  csb 3395  csn 3998  cop 4004  ciun 4299   cmpt 4482   cxp 4851  cfv 5601   cmpt2 6307  c1st 6805  c2nd 6806 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-8 1874  ax-9 1876  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401  ax-sep 4546  ax-nul 4555  ax-pow 4602  ax-pr 4660  ax-un 6597 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-fal 1443  df-ex 1658  df-nf 1662  df-sb 1791  df-eu 2273  df-mo 2274  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ne 2616  df-ral 2776  df-rex 2777  df-reu 2778  df-rab 2780  df-v 3082  df-sbc 3300  df-csb 3396  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-if 3912  df-sn 3999  df-pr 4001  df-op 4005  df-uni 4220  df-iun 4301  df-br 4424  df-opab 4483  df-mpt 4484  df-id 4768  df-xp 4859  df-rel 4860  df-cnv 4861  df-co 4862  df-dm 4863  df-rn 4864  df-iota 5565  df-fun 5603  df-fn 5604  df-f 5605  df-f1 5606  df-fo 5607  df-f1o 5608  df-fv 5609  df-oprab 6309  df-mpt2 6310  df-1st 6807  df-2nd 6808 This theorem is referenced by:  fpar  6911
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