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Mirrors > Home > ILE Home > Th. List > 3anbi123d | Unicode version |
Description: Deduction joining 3 equivalences to form equivalence of conjunctions. (Contributed by NM, 22-Apr-1994.) |
Ref | Expression |
---|---|
bi3d.1 |
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bi3d.2 |
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bi3d.3 |
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Ref | Expression |
---|---|
3anbi123d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi3d.1 |
. . . 4
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2 | bi3d.2 |
. . . 4
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3 | 1, 2 | anbi12d 465 |
. . 3
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4 | bi3d.3 |
. . 3
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5 | 3, 4 | anbi12d 465 |
. 2
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6 | df-3an 965 |
. 2
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7 | df-3an 965 |
. 2
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8 | 5, 6, 7 | 3bitr4g 222 |
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 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-3an 965 |
This theorem is referenced by: 3anbi12d 1292 3anbi13d 1293 3anbi23d 1294 limeq 4307 smoeq 6195 tfrlemi1 6237 tfr1onlemaccex 6253 tfrcllemaccex 6266 ereq1 6444 updjud 6975 ctssdclemr 7005 elinp 7306 sup3exmid 8739 iccshftr 9807 iccshftl 9809 iccdil 9811 icccntr 9813 fzaddel 9870 elfzomelpfzo 10039 seq3f1olemstep 10305 seq3f1olemp 10306 sumeq1 11156 summodclem2 11183 summodc 11184 zsumdc 11185 prodmodclem2 11378 prodmodc 11379 divalglemnn 11651 divalglemeunn 11654 divalglemeuneg 11656 dfgcd2 11738 ctiunct 11989 isstruct2im 12008 isstruct2r 12009 fiinopn 12210 lmfval 12400 upxp 12480 2irrexpqap 13103 dceqnconst 13423 |
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