ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfov GIF version

Theorem nfov 5767
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 5766 . 2 (⊤ → 𝑥(𝐴𝐹𝐵))
87mptru 1323 1 𝑥(𝐴𝐹𝐵)
Colors of variables: wff set class
Syntax hints:  wtru 1315  wnfc 2243  (class class class)co 5740
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rex 2397  df-v 2660  df-un 3043  df-sn 3501  df-pr 3502  df-op 3504  df-uni 3705  df-br 3898  df-iota 5056  df-fv 5099  df-ov 5743
This theorem is referenced by:  csbov123g  5775  ovmpos  5860  ov2gf  5861  ovmpodxf  5862  ovmpodv2  5870  ovi3  5873  nfof  5953  offval2  5963  caucvgprprlemaddq  7480  nfseq  10179  fsumadd  11126  mertenslem2  11256  oddpwdclemdvds  11754  oddpwdclemndvds  11755  cnmpt2t  12368  cnmptcom  12373  fsumcncntop  12631
  Copyright terms: Public domain W3C validator