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Theorem nfmpt 3890
 Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by NM, 20-Feb-2013.)
Hypotheses
Ref Expression
nfmpt.1
nfmpt.2
Assertion
Ref Expression
nfmpt
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem nfmpt
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-mpt 3861 . 2
2 nfmpt.1 . . . . 5
32nfcri 2217 . . . 4
4 nfmpt.2 . . . . 5
54nfeq2 2234 . . . 4
63, 5nfan 1498 . . 3
76nfopab 3866 . 2
81, 7nfcxfr 2220 1
 Colors of variables: wff set class Syntax hints:   wa 102   wceq 1285   wcel 1434  wnfc 2210  copab 3858   cmpt 3859 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-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-opab 3860  df-mpt 3861 This theorem is referenced by:  nffrec  6066  nfsum1  10412  nfsum  10413
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