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Theorem mpteq12f 4277
 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 1806 . . . 4
2 nfra1 2748 . . . 4
31, 2nfan 1846 . . 3
4 nfv 1629 . . 3
5 rsp 2758 . . . . . . 7
65imp 419 . . . . . 6
76eqeq2d 2446 . . . . 5
87pm5.32da 623 . . . 4
9 sp 1763 . . . . . 6
109eleq2d 2502 . . . . 5
1110anbi1d 686 . . . 4
128, 11sylan9bbr 682 . . 3
133, 4, 12opabbid 4262 . 2
14 df-mpt 4260 . 2
15 df-mpt 4260 . 2
1613, 14, 153eqtr4g 2492 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wal 1549   wceq 1652   wcel 1725  wral 2697  copab 4257   cmpt 4258 This theorem is referenced by:  mpteq12dva  4278  mpteq12  4280  mpteq2ia  4283  mpteq2da  4286  esumeq12dvaf  24420  refsum2cnlem1  27675 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-ral 2702  df-opab 4259  df-mpt 4260
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