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Mirrors > Home > ILE Home > Th. List > df-3an | Unicode version |
Description: Define conjunction ('and') of 3 wff.s. Definition *4.34 of [WhiteheadRussell] p. 118. This abbreviation reduces the number of parentheses and emphasizes that the order of bracketing is not important by virtue of the associative law anass 401. (Contributed by NM, 8-Apr-1994.) |
Ref | Expression |
---|---|
df-3an |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph |
. . 3
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2 | wps |
. . 3
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3 | wch |
. . 3
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4 | 1, 2, 3 | w3a 978 |
. 2
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5 | 1, 2 | wa 104 |
. . 3
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6 | 5, 3 | wa 104 |
. 2
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7 | 4, 6 | wb 105 |
1
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Colors of variables: wff set class |
This definition is referenced by: 3anass 982 3anrot 983 3ancoma 985 3anan32 989 3ioran 993 3simpa 994 3pm3.2i 1175 pm3.2an3 1176 3jca 1177 3anbi123i 1188 3imp 1193 3anbi123d 1312 3anim123d 1319 an6 1321 19.26-3an 1483 hb3an 1550 nf3an 1566 nf3and 1569 eeeanv 1933 sb3an 1958 mopick2 2109 r19.26-3 2607 3reeanv 2648 ceqsex3v 2780 ceqsex4v 2781 ceqsex8v 2783 sbc3an 3025 elin3 3327 rexdifpr 3621 raltpg 3646 tpss 3759 dfopg 3777 opeq1 3779 opeq2 3780 opm 4235 otth2 4242 poirr 4308 po3nr 4311 wepo 4360 wetrep 4361 rabxp 4664 brinxp2 4694 brinxp 4695 sotri2 5027 sotri3 5028 f1orn 5472 dff1o6 5777 isosolem 5825 oprabid 5907 caovimo 6068 elovmpo 6072 dfxp3 6195 nnaord 6510 fiintim 6928 prmuloc 7565 ltrelxr 8018 rexuz2 9581 ltxr 9775 elixx3g 9901 elioo4g 9934 elioopnf 9967 elioomnf 9968 elicopnf 9969 elxrge0 9978 divelunit 10002 elfz2 10015 elfzuzb 10019 uzsplit 10092 fznn0 10113 elfzmlbp 10132 elfzo2 10150 fzolb2 10154 fzouzsplit 10179 ssfzo12bi 10225 fzind2 10239 dfrp2 10264 abs2dif 11115 sumeq2 11367 divalgb 11930 divgcdz 11972 rplpwr 12028 nnwosdc 12040 cncongr1 12103 pythagtriplem2 12266 pythagtrip 12283 xpscf 12766 issubm2 12864 issubg3 13052 resgrpisgrp 13055 eqgval 13082 eqger 13083 ringpropd 13217 isbasis3g 13549 lmfval 13695 lmbr 13716 lmbr2 13717 xmeterval 13938 xmeter 13939 cnbl0 14037 cnblcld 14038 limcrcl 14130 bd3an 14585 |
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