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Theorem mpteq12d 25384
 Description: An equality inference for the maps to notation. Compare mpteq12dv 4279. (Contributed by Scott Fenton, 8-Aug-2013.) (Revised by Mario Carneiro, 11-Dec-2016.)
Hypotheses
Ref Expression
mpteq12d.1
mpteq12d.3
mpteq12d.4
Assertion
Ref Expression
mpteq12d

Proof of Theorem mpteq12d
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 mpteq12d.1 . . 3
2 nfv 1629 . . 3
3 mpteq12d.3 . . . . 5
43eleq2d 2502 . . . 4
5 mpteq12d.4 . . . . 5
65eqeq2d 2446 . . . 4
74, 6anbi12d 692 . . 3
81, 2, 7opabbid 4262 . 2
9 df-mpt 4260 . 2
10 df-mpt 4260 . 2
118, 9, 103eqtr4g 2492 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wnf 1553   wceq 1652   wcel 1725  copab 4257   cmpt 4258 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-opab 4259  df-mpt 4260
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