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Theorem nfmpt2 5625
 Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by NM, 20-Feb-2013.)
Hypotheses
Ref Expression
nfmpt2.1
nfmpt2.2
nfmpt2.3
Assertion
Ref Expression
nfmpt2
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)   (,,)   (,,)

Proof of Theorem nfmpt2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-mpt2 5569 . 2
2 nfmpt2.1 . . . . . 6
32nfcri 2217 . . . . 5
4 nfmpt2.2 . . . . . 6
54nfcri 2217 . . . . 5
63, 5nfan 1498 . . . 4
7 nfmpt2.3 . . . . 5
87nfeq2 2234 . . . 4
96, 8nfan 1498 . . 3
109nfoprab 5609 . 2
111, 10nfcxfr 2220 1
 Colors of variables: wff set class Syntax hints:   wa 102   wceq 1285   wcel 1434  wnfc 2210  coprab 5565   cmpt2 5566 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-oprab 5568  df-mpt2 5569 This theorem is referenced by:  nfiseq  9598
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