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Theorem mpoeq123dva 5872
 Description: An equality deduction for the maps-to notation. (Contributed by Mario Carneiro, 26-Jan-2017.)
Hypotheses
Ref Expression
mpoeq123dv.1
mpoeq123dva.2
mpoeq123dva.3
Assertion
Ref Expression
mpoeq123dva
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)   (,)   (,)   (,)   (,)

Proof of Theorem mpoeq123dva
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 mpoeq123dva.3 . . . . . 6
21eqeq2d 2166 . . . . 5
32pm5.32da 448 . . . 4
4 mpoeq123dva.2 . . . . . . . 8
54eleq2d 2224 . . . . . . 7
65pm5.32da 448 . . . . . 6
7 mpoeq123dv.1 . . . . . . . 8
87eleq2d 2224 . . . . . . 7
98anbi1d 461 . . . . . 6
106, 9bitrd 187 . . . . 5
1110anbi1d 461 . . . 4
123, 11bitrd 187 . . 3
1312oprabbidv 5865 . 2
14 df-mpo 5819 . 2
15 df-mpo 5819 . 2
1613, 14, 153eqtr4g 2212 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1332   wcel 2125  coprab 5815   cmpo 5816 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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-11 1483  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-oprab 5818  df-mpo 5819 This theorem is referenced by:  mpoeq123dv  5873
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