New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  mpteq12f Unicode version

Theorem mpteq12f 5655
 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 1788 . . . 4
2 nfra1 2664 . . . 4
31, 2nfan 1824 . . 3
4 nfv 1619 . . 3
5 rsp 2674 . . . . . . 7
65imp 418 . . . . . 6
76eqeq2d 2364 . . . . 5
87pm5.32da 622 . . . 4
9 sp 1747 . . . . . 6
109eleq2d 2420 . . . . 5
1110anbi1d 685 . . . 4
128, 11sylan9bbr 681 . . 3
133, 4, 12opabbid 4624 . 2
14 df-mpt 5652 . 2
15 df-mpt 5652 . 2
1613, 14, 153eqtr4g 2410 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358  wal 1540   wceq 1642   wcel 1710  wral 2614  copab 4622   cmpt 5651 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-ral 2619  df-opab 4623  df-mpt 5652 This theorem is referenced by:  mpteq12dv  5656  mpteq12  5657  mpteq2ia  5659  mpteq2da  5666
 Copyright terms: Public domain W3C validator