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Theorem mpteq12f 4500
 Description: An equality theorem for the maps to notation. (Contributed by Mario Carneiro, 16-Dec-2013.)
Assertion
Ref Expression
mpteq12f

Proof of Theorem mpteq12f
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfa1 1956 . . . 4
2 nfra1 2803 . . . 4
31, 2nfan 1988 . . 3
4 nfv 1755 . . 3
5 rspa 2789 . . . . . 6
65eqeq2d 2436 . . . . 5
76pm5.32da 645 . . . 4
8 sp 1914 . . . . . 6
98eleq2d 2492 . . . . 5
109anbi1d 709 . . . 4
117, 10sylan9bbr 705 . . 3
123, 4, 11opabbid 4486 . 2
13 df-mpt 4484 . 2
14 df-mpt 4484 . 2
1512, 13, 143eqtr4g 2488 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370  wal 1435   wceq 1437   wcel 1872  wral 2771  copab 4481   cmpt 4482 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-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-ral 2776  df-opab 4483  df-mpt 4484 This theorem is referenced by:  mpteq12dva  4501  mpteq12  4503  mpteq2ia  4506  mpteq2da  4509  esumeq12dvaf  28861  refsum2cnlem1  37332
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