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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 442 |
. . 3
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4 | bi3d.3 |
. . 3
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5 | 3, 4 | anbi12d 442 |
. 2
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6 | df-3an 886 |
. 2
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7 | df-3an 886 |
. 2
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8 | 5, 6, 7 | 3bitr4g 212 |
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 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 df-3an 886 |
This theorem is referenced by: 3anbi12d 1207 3anbi13d 1208 3anbi23d 1209 sbc3ang 2814 limeq 4080 smoeq 5846 tfrlemi1 5887 ereq1 6049 elinp 6457 iccshftr 8632 iccshftl 8634 iccdil 8636 icccntr 8638 fzaddel 8692 elfzomelpfzo 8857 |
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