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Theorem nffo 5644
 Description: Bound-variable hypothesis builder for an onto function. (Contributed by NM, 16-May-2004.)
Hypotheses
Ref Expression
nffo.1
nffo.2
nffo.3
Assertion
Ref Expression
nffo

Proof of Theorem nffo
StepHypRef Expression
1 df-fo 5452 . 2
2 nffo.1 . . . 4
3 nffo.2 . . . 4
42, 3nffn 5533 . . 3
52nfrn 5104 . . . 4
6 nffo.3 . . . 4
75, 6nfeq 2578 . . 3
84, 7nfan 1846 . 2
91, 8nfxfr 1579 1
 Colors of variables: wff set class Syntax hints:   wa 359  wnf 1553   wceq 1652  wnfc 2558   crn 4871   wfn 5441  wfo 5444 This theorem is referenced by:  nff1o  5664 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-fun 5448  df-fn 5449  df-fo 5452
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