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Theorem nffv 5491
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 5191 . 2 (𝐹𝐴) = (℩𝑦𝐴𝐹𝑦)
2 nffv.2 . . . 4 𝑥𝐴
3 nffv.1 . . . 4 𝑥𝐹
4 nfcv 2306 . . . 4 𝑥𝑦
52, 3, 4nfbr 4023 . . 3 𝑥 𝐴𝐹𝑦
65nfiotaw 5152 . 2 𝑥(℩𝑦𝐴𝐹𝑦)
71, 6nfcxfr 2303 1 𝑥(𝐹𝐴)
Colors of variables: wff set class
Syntax hints:  wnfc 2293   class class class wbr 3977  cio 5146  cfv 5183
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146
This theorem depends on definitions:  df-bi 116  df-3an 969  df-tru 1345  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-nfc 2295  df-rex 2448  df-v 2724  df-un 3116  df-sn 3577  df-pr 3578  df-op 3580  df-uni 3785  df-br 3978  df-iota 5148  df-fv 5191
This theorem is referenced by:  nffvmpt1  5492  nffvd  5493  dffn5imf  5536  fvmptssdm  5565  fvmptf  5573  eqfnfv2f  5582  ralrnmpt  5622  rexrnmpt  5623  ffnfvf  5639  funiunfvdmf  5727  dff13f  5733  nfiso  5769  nfrecs  6267  nffrec  6356  cc2  7200  nfseq  10381  seq3f1olemstep  10427  seq3f1olemp  10428  nfsum1  11287  nfsum  11288  fsumrelem  11402  nfcprod1  11485  nfcprod  11486  ctiunctlemfo  12335  ctiunct  12336  cnmpt11  12850  cnmpt21  12858
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