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Theorem nff 5732
 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 5597 . 2
2 nff.1 . . . 4
3 nff.2 . . . 4
42, 3nffn 5682 . . 3
52nfrn 5250 . . . 4
6 nff.3 . . . 4
75, 6nfss 3496 . . 3
84, 7nfan 1928 . 2
91, 8nfxfr 1645 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  F/wnf 1616  F/_wnfc 2605  C_wss 3475  rancrn 5005  Fnwfn 5588  -->wf 5589 This theorem is referenced by:  nff1  5784  nfwrd  12569  fcomptf  27503  esumfzf  28075  esumfsup  28076  sdclem1  30236  fmuldfeqlem1  31576  dvnmul  31740  stoweidlem53  31835  stoweidlem54  31836  stoweidlem57  31839 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-fun 5595  df-fn 5596  df-f 5597
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