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Mirrors > Home > ILE Home > Th. List > nfbr | GIF version |
Description: Bound-variable hypothesis builder for binary relation. (Contributed by NM, 1-Sep-1999.) (Revised by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
nfbr.1 | ⊢ Ⅎ𝑥𝐴 |
nfbr.2 | ⊢ Ⅎ𝑥𝑅 |
nfbr.3 | ⊢ Ⅎ𝑥𝐵 |
Ref | Expression |
---|---|
nfbr | ⊢ Ⅎ𝑥 𝐴𝑅𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfbr.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
2 | 1 | a1i 9 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐴) |
3 | nfbr.2 | . . . 4 ⊢ Ⅎ𝑥𝑅 | |
4 | 3 | a1i 9 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝑅) |
5 | nfbr.3 | . . . 4 ⊢ Ⅎ𝑥𝐵 | |
6 | 5 | a1i 9 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐵) |
7 | 2, 4, 6 | nfbrd 3973 | . 2 ⊢ (⊤ → Ⅎ𝑥 𝐴𝑅𝐵) |
8 | 7 | mptru 1340 | 1 ⊢ Ⅎ𝑥 𝐴𝑅𝐵 |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1332 Ⅎwnf 1436 Ⅎwnfc 2268 class class class wbr 3929 |
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-v 2688 df-un 3075 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 |
This theorem is referenced by: sbcbrg 3982 nfpo 4223 nfso 4224 pofun 4234 nfse 4263 nffrfor 4270 nfwe 4277 nfco 4704 nfcnv 4718 dfdmf 4732 dfrnf 4780 nfdm 4783 dffun6f 5136 dffun4f 5139 nffv 5431 funfvdm2f 5486 fvmptss2 5496 f1ompt 5571 fmptco 5586 nfiso 5707 nfofr 5988 ofrfval2 5998 tposoprab 6177 xpcomco 6720 nfsup 6879 caucvgprprlemaddq 7516 lble 8705 nfsum1 11125 nfsum 11126 fsum00 11231 mertenslem2 11305 nfcprod1 11323 nfcprod 11324 oddpwdclemdvds 11848 oddpwdclemndvds 11849 |
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