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Theorem nffv 5185
 Description: Bound-variable hypothesis builder for function value. (Contributed by NM, 14-Nov-1995.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
nffv.1
nffv.2
Assertion
Ref Expression
nffv

Proof of Theorem nffv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-fv 4910 . 2
2 nffv.2 . . . 4
3 nffv.1 . . . 4
4 nfcv 2178 . . . 4
52, 3, 4nfbr 3808 . . 3
65nfiotaxy 4871 . 2
71, 6nfcxfr 2175 1
 Colors of variables: wff set class Syntax hints:  wnfc 2165   class class class wbr 3764  cio 4865  cfv 4902 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910 This theorem is referenced by:  nffvmpt1  5186  nffvd  5187  dffn5imf  5228  fvmptssdm  5255  fvmptf  5263  eqfnfv2f  5269  ralrnmpt  5309  rexrnmpt  5310  ffnfvf  5324  funiunfvdmf  5403  dff13f  5409  nfiso  5446  nfrecs  5922  nffrec  5982  nfiseq  9218  nfsum1  9875  nfsum  9876
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