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Mirrors > Home > ILE Home > Th. List > anass | Unicode version |
Description: Associative law for conjunction. Theorem *4.32 of [WhiteheadRussell] p. 118. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 24-Nov-2012.) |
Ref | Expression |
---|---|
anass |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 |
. . 3
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2 | 1 | anassrs 400 |
. 2
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3 | id 19 |
. . 3
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4 | 3 | anasss 399 |
. 2
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5 | 2, 4 | impbii 126 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: bianass 469 mpan10 474 an12 561 an32 562 an13 563 an31 564 an4 586 3anass 982 sbidm 1851 4exdistr 1916 2sb5 1983 2sb5rf 1989 sbel2x 1998 r2exf 2495 r19.41 2632 ceqsex3v 2781 ceqsrex2v 2871 rexrab 2902 rexrab2 2906 rexss 3224 inass 3347 difin2 3399 difrab 3411 reupick3 3422 inssdif0im 3492 rexdifpr 3622 rexdifsn 3726 unidif0 4169 bnd2 4175 eqvinop 4245 copsexg 4246 uniuni 4453 rabxp 4665 elvvv 4691 rexiunxp 4771 resopab2 4956 ssrnres 5073 elxp4 5118 elxp5 5119 cnvresima 5120 mptpreima 5124 coass 5149 dff1o2 5468 eqfnfv3 5617 rexsupp 5642 isoini 5821 f1oiso 5829 oprabid 5909 dfoprab2 5924 mpoeq123 5936 mpomptx 5968 resoprab2 5974 ovi3 6013 oprabex3 6132 spc2ed 6236 f1od2 6238 brtpos2 6254 mapsnen 6813 xpsnen 6823 xpcomco 6828 xpassen 6832 ltexpi 7338 enq0enq 7432 enq0tr 7435 prnmaxl 7489 prnminu 7490 genpdflem 7508 ltexprlemm 7601 suplocsrlemb 7807 axaddf 7869 axmulf 7870 rexuz 9582 rexuz2 9583 rexrp 9678 elixx3g 9903 elfz2 10017 fzdifsuc 10083 fzind2 10241 divalgb 11932 gcdass 12018 nnwosdc 12042 lcmass 12087 isprm2 12119 infpn2 12459 issubg3 13057 ntreq0 13671 tx1cn 13808 tx2cn 13809 blres 13973 metrest 14045 elcncf1di 14105 dedekindicclemicc 14149 |
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