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Theorem mpt2eq123i 5510
Description: An equality inference for the maps to notation. (Contributed by NM, 15-Jul-2013.)
Hypotheses
Ref Expression
mpt2eq123i.1  D
mpt2eq123i.2  E
mpt2eq123i.3  C  F
Assertion
Ref Expression
mpt2eq123i  ,  |->  C  D ,  E  |->  F

Proof of Theorem mpt2eq123i
StepHypRef Expression
1 mpt2eq123i.1 . . . 4  D
21a1i 9 . . 3  D
3 mpt2eq123i.2 . . . 4  E
43a1i 9 . . 3  E
5 mpt2eq123i.3 . . . 4  C  F
65a1i 9 . . 3  C  F
72, 4, 6mpt2eq123dv 5509 . 2  ,  |->  C  D ,  E  |->  F
87trud 1251 1  ,  |->  C  D ,  E  |->  F
Colors of variables: wff set class
Syntax hints:   wceq 1242   wtru 1243    |-> cmpt2 5457
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-oprab 5459  df-mpt2 5460
This theorem is referenced by:  ofmres  5705
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