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Mirrors > Home > ILE Home > Th. List > nfov | GIF version |
Description: Bound-variable hypothesis builder for operation value. (Contributed by NM, 4-May-2004.) |
Ref | Expression |
---|---|
nfov.1 | ⊢ Ⅎ𝑥𝐴 |
nfov.2 | ⊢ Ⅎ𝑥𝐹 |
nfov.3 | ⊢ Ⅎ𝑥𝐵 |
Ref | Expression |
---|---|
nfov | ⊢ Ⅎ𝑥(𝐴𝐹𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfov.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
2 | 1 | a1i 9 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐴) |
3 | nfov.2 | . . . 4 ⊢ Ⅎ𝑥𝐹 | |
4 | 3 | a1i 9 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐹) |
5 | nfov.3 | . . . 4 ⊢ Ⅎ𝑥𝐵 | |
6 | 5 | a1i 9 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐵) |
7 | 2, 4, 6 | nfovd 5800 | . 2 ⊢ (⊤ → Ⅎ𝑥(𝐴𝐹𝐵)) |
8 | 7 | mptru 1340 | 1 ⊢ Ⅎ𝑥(𝐴𝐹𝐵) |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1332 Ⅎwnfc 2268 (class class class)co 5774 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-v 2688 df-un 3075 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-iota 5088 df-fv 5131 df-ov 5777 |
This theorem is referenced by: csbov123g 5809 ovmpos 5894 ov2gf 5895 ovmpodxf 5896 ovmpodv2 5904 ovi3 5907 nfof 5987 offval2 5997 caucvgprprlemaddq 7516 nfseq 10228 fsumadd 11175 mertenslem2 11305 oddpwdclemdvds 11848 oddpwdclemndvds 11849 cnmpt2t 12462 cnmptcom 12467 fsumcncntop 12725 |
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