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Theorem mpoeq12 5824
 Description: An equality theorem for the maps-to notation. (Contributed by Mario Carneiro, 16-Dec-2013.)
Assertion
Ref Expression
mpoeq12
Distinct variable groups:   ,,   ,,   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem mpoeq12
StepHypRef Expression
1 eqid 2137 . . . . 5
21rgenw 2485 . . . 4
32jctr 313 . . 3
43ralrimivw 2504 . 2
5 mpoeq123 5823 . 2
64, 5sylan2 284 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1331  wral 2414   cmpo 5769 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 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-oprab 5771  df-mpo 5772 This theorem is referenced by:  seqeq1  10214  txvalex  12412  txval  12413
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