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Theorem mpteq12dva 4289
 Description: An equality inference for the maps to notation. (Contributed by Mario Carneiro, 26-Jan-2017.)
Hypotheses
Ref Expression
mpteq12dv.1
mpteq12dva.2
Assertion
Ref Expression
mpteq12dva
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem mpteq12dva
StepHypRef Expression
1 mpteq12dv.1 . . 3
21alrimiv 1642 . 2
3 mpteq12dva.2 . . 3
43ralrimiva 2791 . 2
5 mpteq12f 4288 . 2
62, 4, 5syl2anc 644 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360  wal 1550   wceq 1653   wcel 1726  wral 2707   cmpt 4269 This theorem is referenced by:  mpteq12dv  4290  cidpropd  13941  monpropd  13968  fucpropd  14179  curfpropd  14335  hofpropd  14369  yonffthlem  14384  ofcfval  24486  ovmpt3rab1  28106  elovmpt3rab  28108  elovmptnn0wrd  28214 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-ral 2712  df-opab 4270  df-mpt 4271
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