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Theorem nffn 5533
 Description: Bound-variable hypothesis builder for a function with domain. (Contributed by NM, 30-Jan-2004.)
Hypotheses
Ref Expression
nffn.1
nffn.2
Assertion
Ref Expression
nffn

Proof of Theorem nffn
StepHypRef Expression
1 df-fn 5449 . 2
2 nffn.1 . . . 4
32nffun 5468 . . 3
42nfdm 5103 . . . 4
5 nffn.2 . . . 4
64, 5nfeq 2578 . . 3
73, 6nfan 1846 . 2
81, 7nfxfr 1579 1
 Colors of variables: wff set class Syntax hints:   wa 359  wnf 1553   wceq 1652  wnfc 2558   cdm 4870   wfun 5440   wfn 5441 This theorem is referenced by:  nff  5581  nffo  5644  nfixp  7073  nfixp1  7074  feqmptdf  24067  stoweidlem31  27747  stoweidlem35  27751  stoweidlem59  27775  bnj1463  29361 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-fun 5448  df-fn 5449
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