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Theorem nfov 5679
Description: Bound-variable hypothesis builder for operation value. (Contributed by NM, 4-May-2004.)
Hypotheses
Ref Expression
nfov.1 𝑥𝐴
nfov.2 𝑥𝐹
nfov.3 𝑥𝐵
Assertion
Ref Expression
nfov 𝑥(𝐴𝐹𝐵)

Proof of Theorem nfov
StepHypRef Expression
1 nfov.1 . . . 4 𝑥𝐴
21a1i 9 . . 3 (⊤ → 𝑥𝐴)
3 nfov.2 . . . 4 𝑥𝐹
43a1i 9 . . 3 (⊤ → 𝑥𝐹)
5 nfov.3 . . . 4 𝑥𝐵
65a1i 9 . . 3 (⊤ → 𝑥𝐵)
72, 4, 6nfovd 5678 . 2 (⊤ → 𝑥(𝐴𝐹𝐵))
87mptru 1298 1 𝑥(𝐴𝐹𝐵)
Colors of variables: wff set class
Syntax hints:  wtru 1290  wnfc 2215  (class class class)co 5652
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 3003  df-sn 3452  df-pr 3453  df-op 3455  df-uni 3654  df-br 3846  df-iota 4980  df-fv 5023  df-ov 5655
This theorem is referenced by:  csbov123g  5687  ovmpt2s  5768  ov2gf  5769  ovmpt2dxf  5770  ovmpt2dv2  5778  ovi3  5781  nfof  5861  offval2  5870  caucvgprprlemaddq  7267  nfiseq  9868  fsumadd  10800  isummulc2  10820  mertenslem2  10930  oddpwdclemdvds  11426  oddpwdclemndvds  11427
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