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Theorem mpteq12f 4018
 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 1518 . . . 4
2 nfra1 2471 . . . 4
31, 2nfan 1541 . . 3
4 nfv 1505 . . 3
5 rsp 2485 . . . . . . 7
65imp 123 . . . . . 6
76eqeq2d 2153 . . . . 5
87pm5.32da 448 . . . 4
9 sp 1488 . . . . . 6
109eleq2d 2211 . . . . 5
1110anbi1d 461 . . . 4
128, 11sylan9bbr 459 . . 3
133, 4, 12opabbid 4003 . 2
14 df-mpt 4001 . 2
15 df-mpt 4001 . 2
1613, 14, 153eqtr4g 2199 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103  wal 1330   wceq 1332   wcel 2112  wral 2418  copab 3998   cmpt 3999 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-11 1483  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1732  df-clab 2128  df-cleq 2134  df-clel 2137  df-ral 2423  df-opab 4000  df-mpt 4001 This theorem is referenced by:  mpteq12dva  4019  mpteq12  4021  mpteq2ia  4024  mpteq2da  4027
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