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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 3943 | . 2 ⊢ (⊤ → Ⅎ𝑥 𝐴𝑅𝐵) |
8 | 7 | mptru 1325 | 1 ⊢ Ⅎ𝑥 𝐴𝑅𝐵 |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1317 Ⅎwnf 1421 Ⅎwnfc 2245 class class class wbr 3899 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 |
This theorem is referenced by: sbcbrg 3952 nfpo 4193 nfso 4194 pofun 4204 nfse 4233 nffrfor 4240 nfwe 4247 nfco 4674 nfcnv 4688 dfdmf 4702 dfrnf 4750 nfdm 4753 dffun6f 5106 dffun4f 5109 nffv 5399 funfvdm2f 5454 fvmptss2 5464 f1ompt 5539 fmptco 5554 nfiso 5675 nfofr 5956 ofrfval2 5966 tposoprab 6145 xpcomco 6688 nfsup 6847 caucvgprprlemaddq 7484 lble 8673 nfsum1 11093 nfsum 11094 fsum00 11199 mertenslem2 11273 oddpwdclemdvds 11775 oddpwdclemndvds 11776 |
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