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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 300 | . 2 |
4 | mpbi2and.3 | . 2 | |
5 | 3, 4 | mpbid 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: supisoti 6423 remim 9747 resqrtcl 9915 divalgmod 10327 oddpwdclemxy 10547 |
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