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Mirrors > Home > ILE Home > Th. List > nfbr | Unicode 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 |
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nfbr.2 |
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nfbr.3 |
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Ref | Expression |
---|---|
nfbr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfbr.1 |
. . . 4
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2 | 1 | a1i 9 |
. . 3
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3 | nfbr.2 |
. . . 4
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4 | 3 | a1i 9 |
. . 3
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5 | nfbr.3 |
. . . 4
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6 | 5 | a1i 9 |
. . 3
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7 | 2, 4, 6 | nfbrd 3894 |
. 2
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8 | 7 | mptru 1299 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-v 2622 df-un 3004 df-sn 3456 df-pr 3457 df-op 3459 df-br 3852 |
This theorem is referenced by: sbcbrg 3900 nfpo 4137 nfso 4138 pofun 4148 nfse 4177 nffrfor 4184 nfwe 4191 nfco 4614 nfcnv 4628 dfdmf 4642 dfrnf 4689 nfdm 4692 dffun6f 5041 dffun4f 5044 nffv 5328 funfvdm2f 5382 fvmptss2 5392 f1ompt 5464 fmptco 5478 nfiso 5599 nfofr 5876 ofrfval2 5885 tposoprab 6059 xpcomco 6596 nfsup 6741 caucvgprprlemaddq 7328 lble 8469 nfsum1 10806 nfsum 10807 fsum00 10917 mertenslem2 10991 oddpwdclemdvds 11487 oddpwdclemndvds 11488 |
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