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Theorem nff 5171
 Description: Bound-variable hypothesis builder for a mapping. (Contributed by NM, 29-Jan-2004.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
nff.1
nff.2
nff.3
Assertion
Ref Expression
nff

Proof of Theorem nff
StepHypRef Expression
1 df-f 5032 . 2
2 nff.1 . . . 4
3 nff.2 . . . 4
42, 3nffn 5123 . . 3
52nfrn 4693 . . . 4
6 nff.3 . . . 4
75, 6nfss 3019 . . 3
84, 7nfan 1503 . 2
91, 8nfxfr 1409 1
 Colors of variables: wff set class Syntax hints:   wa 103  wnf 1395  wnfc 2216   wss 3000   crn 4453   wfn 5023  wf 5024 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ral 2365  df-v 2622  df-un 3004  df-in 3006  df-ss 3013  df-sn 3456  df-pr 3457  df-op 3459  df-br 3852  df-opab 3906  df-rel 4459  df-cnv 4460  df-co 4461  df-dm 4462  df-rn 4463  df-fun 5030  df-fn 5031  df-f 5032 This theorem is referenced by:  nff1  5227
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