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Theorem nfmpt 4023
 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 3994 . 2
2 nfmpt.1 . . . . 5
32nfcri 2275 . . . 4
4 nfmpt.2 . . . . 5
54nfeq2 2293 . . . 4
63, 5nfan 1544 . . 3
76nfopab 3999 . 2
81, 7nfcxfr 2278 1
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1331   wcel 1480  wnfc 2268  copab 3991   cmpt 3992 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-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-opab 3993  df-mpt 3994 This theorem is referenced by:  nfof  5990  nffrec  6296  mapxpen  6745  nfsum1  11149  nfsum  11150  nfcprod1  11347  nfcprod  11348  ctiunct  11976  fsumcncntop  12751  limcmpted  12827
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