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Mirrors > Home > ILE Home > Th. List > mpbir3and | Unicode version |
Description: Detach a conjunction of truths in a biconditional. (Contributed by Mario Carneiro, 11-May-2014.) |
Ref | Expression |
---|---|
mpbir3and.1 | |
mpbir3and.2 | |
mpbir3and.3 | |
mpbir3and.4 |
Ref | Expression |
---|---|
mpbir3and |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpbir3and.1 | . . 3 | |
2 | mpbir3and.2 | . . 3 | |
3 | mpbir3and.3 | . . 3 | |
4 | 1, 2, 3 | 3jca 1084 | . 2 |
5 | mpbir3and.4 | . 2 | |
6 | 4, 5 | mpbird 156 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 w3a 885 |
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 887 |
This theorem is referenced by: ixxss1 8773 ixxss2 8774 ixxss12 8775 ubioc1 8798 lbico1 8799 lbicc2 8852 ubicc2 8853 modqelico 9176 |
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