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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 4048 | . 2 ⊢ (⊤ → Ⅎ𝑥 𝐴𝑅𝐵) |
8 | 7 | mptru 1362 | 1 ⊢ Ⅎ𝑥 𝐴𝑅𝐵 |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1354 Ⅎwnf 1460 Ⅎwnfc 2306 class class class wbr 4003 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-sn 3598 df-pr 3599 df-op 3601 df-br 4004 |
This theorem is referenced by: sbcbrg 4057 nfpo 4301 nfso 4302 pofun 4312 nfse 4341 nffrfor 4348 nfwe 4355 nfco 4792 nfcnv 4806 dfdmf 4820 dfrnf 4868 nfdm 4871 dffun6f 5229 dffun4f 5232 nffv 5525 funfvdm2f 5581 fvmptss2 5591 f1ompt 5667 fmptco 5682 nfiso 5806 nfofr 6088 ofrfval2 6098 tposoprab 6280 xpcomco 6825 nfsup 6990 caucvgprprlemaddq 7706 lble 8903 nfsum1 11363 nfsum 11364 fsum00 11469 mertenslem2 11543 nfcprod1 11561 nfcprod 11562 fprodap0 11628 fprodrec 11636 fproddivapf 11638 fprodap0f 11643 fprodle 11647 oddpwdclemdvds 12169 oddpwdclemndvds 12170 |
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