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Theorem nffv 5299
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 𝑥𝐹
nffv.2 𝑥𝐴
Assertion
Ref Expression
nffv 𝑥(𝐹𝐴)

Proof of Theorem nffv
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 df-fv 5010 . 2 (𝐹𝐴) = (℩𝑦𝐴𝐹𝑦)
2 nffv.2 . . . 4 𝑥𝐴
3 nffv.1 . . . 4 𝑥𝐹
4 nfcv 2228 . . . 4 𝑥𝑦
52, 3, 4nfbr 3881 . . 3 𝑥 𝐴𝐹𝑦
65nfiotaxy 4971 . 2 𝑥(℩𝑦𝐴𝐹𝑦)
71, 6nfcxfr 2225 1 𝑥(𝐹𝐴)
Colors of variables: wff set class
Syntax hints:  wnfc 2215   class class class wbr 3837  cio 4965  cfv 5002
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365  df-v 2621  df-un 3001  df-sn 3447  df-pr 3448  df-op 3450  df-uni 3649  df-br 3838  df-iota 4967  df-fv 5010
This theorem is referenced by:  nffvmpt1  5300  nffvd  5301  dffn5imf  5343  fvmptssdm  5371  fvmptf  5379  eqfnfv2f  5385  ralrnmpt  5425  rexrnmpt  5426  ffnfvf  5441  funiunfvdmf  5525  dff13f  5531  nfiso  5567  nfrecs  6054  nffrec  6143  nfiseq  9833  seq3f1olemstep  9895  seq3f1olemp  9896  nfsum1  10709  nfsum  10710  fsumrelem  10828
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