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Mirrors > Home > ILE Home > Th. List > mpbi2and | Unicode version |
Description: Detach a conjunction of truths in a biconditional. (Contributed by NM, 6-Nov-2011.) (Proof shortened by Wolf Lammen, 24-Nov-2012.) |
Ref | Expression |
---|---|
mpbi2and.1 |
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mpbi2and.2 |
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mpbi2and.3 |
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Ref | Expression |
---|---|
mpbi2and |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpbi2and.1 |
. . 3
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2 | mpbi2and.2 |
. . 3
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3 | 1, 2 | jca 304 |
. 2
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4 | mpbi2and.3 |
. 2
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5 | 3, 4 | mpbid 146 |
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-ia3 107 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: supisoti 6905 remim 10664 resqrtcl 10833 divalgmod 11660 oddpwdclemxy 11883 divnumden 11910 numdensq 11916 topgele 12235 lmcn2 12488 |
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