MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  mpteq12f Unicode version

Theorem mpteq12f 4528
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 1897 . . . 4
2 nfra1 2838 . . . 4
31, 2nfan 1928 . . 3
4 nfv 1707 . . 3
5 rspa 2824 . . . . . 6
65eqeq2d 2471 . . . . 5
76pm5.32da 641 . . . 4
8 sp 1859 . . . . . 6
98eleq2d 2527 . . . . 5
109anbi1d 704 . . . 4
117, 10sylan9bbr 700 . . 3
123, 4, 11opabbid 4514 . 2
13 df-mpt 4512 . 2
14 df-mpt 4512 . 2
1512, 13, 143eqtr4g 2523 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818  A.wral 2807  {copab 4509  e.cmpt 4510
This theorem is referenced by:  mpteq12dva  4529  mpteq12  4531  mpteq2ia  4534  mpteq2da  4537  esumeq12dvaf  28044  refsum2cnlem1  31412
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812  df-opab 4511  df-mpt 4512
  Copyright terms: Public domain W3C validator