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Theorem nff1 5784
 Description: Bound-variable hypothesis builder for a one-to-one function. (Contributed by NM, 16-May-2004.)
Hypotheses
Ref Expression
nff1.1
nff1.2
nff1.3
Assertion
Ref Expression
nff1

Proof of Theorem nff1
StepHypRef Expression
1 df-f1 5598 . 2
2 nff1.1 . . . 4
3 nff1.2 . . . 4
4 nff1.3 . . . 4
52, 3, 4nff 5732 . . 3
62nfcnv 5186 . . . 4
76nffun 5615 . . 3
85, 7nfan 1928 . 2
91, 8nfxfr 1645 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  F/wnf 1616  F/_wnfc 2605  'ccnv 5003  Funwfun 5587  -->wf 5589  -1-1->`wf1 5590 This theorem is referenced by:  nff1o  5819  iundom2g  8936 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  df-f1 5598
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