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Theorem mpoeq123i 5834
 Description: An equality inference for the maps-to notation. (Contributed by NM, 15-Jul-2013.)
Hypotheses
Ref Expression
mpoeq123i.1
mpoeq123i.2
mpoeq123i.3
Assertion
Ref Expression
mpoeq123i

Proof of Theorem mpoeq123i
StepHypRef Expression
1 mpoeq123i.1 . . . 4
21a1i 9 . . 3
3 mpoeq123i.2 . . . 4
43a1i 9 . . 3
5 mpoeq123i.3 . . . 4
65a1i 9 . . 3
72, 4, 6mpoeq123dv 5833 . 2
87mptru 1340 1
 Colors of variables: wff set class Syntax hints:   wceq 1331   wtru 1332   cmpo 5776 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 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-oprab 5778  df-mpo 5779 This theorem is referenced by:  ofmres  6034
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