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Theorem reldmmpt2 5643
 Description: The domain of an operation defined by maps-to notation is a relation. (Contributed by Stefan O'Rear, 27-Nov-2014.)
Hypothesis
Ref Expression
rngop.1
Assertion
Ref Expression
reldmmpt2
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   (,)   (,)   (,)

Proof of Theorem reldmmpt2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 reldmoprab 5620 . 2
2 rngop.1 . . . . 5
3 df-mpt2 5548 . . . . 5
42, 3eqtri 2102 . . . 4
54dmeqi 4564 . . 3
65releqi 4449 . 2
71, 6mpbir 144 1
 Colors of variables: wff set class Syntax hints:   wa 102   wceq 1285   wcel 1434   cdm 4371   wrel 4376  coprab 5544   cmpt2 5545 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-opab 3848  df-xp 4377  df-rel 4378  df-dm 4381  df-oprab 5547  df-mpt2 5548 This theorem is referenced by: (None)
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