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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 | |
mpbi2and.2 | |
mpbi2and.3 |
Ref | Expression |
---|---|
mpbi2and |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpbi2and.1 | . . 3 | |
2 | mpbi2and.2 | . . 3 | |
3 | 1, 2 | jca 304 | . 2 |
4 | mpbi2and.3 | . 2 | |
5 | 3, 4 | mpbid 146 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 |
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 6983 remim 10811 resqrtcl 10980 divalgmod 11873 oddpwdclemxy 12110 divnumden 12137 numdensq 12143 prmdivdiv 12178 4sqlem7 12323 ismgmid2 12621 mnd1 12666 topgele 12780 lmcn2 13033 |
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