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Theorem mpteq12dva 4045
 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 1854 . 2
3 mpteq12dva.2 . . 3
43ralrimiva 2530 . 2
5 mpteq12f 4044 . 2
62, 4, 5syl2anc 409 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103  wal 1333   wceq 1335   wcel 2128  wral 2435   cmpt 4025 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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-11 1486  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-ral 2440  df-opab 4026  df-mpt 4027 This theorem is referenced by:  mpteq12dv  4046
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