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Mirrors > Home > ILE Home > Th. List > mpbir3an | Unicode version |
Description: Detach a conjunction of truths in a biconditional. (Contributed by NM, 16-Sep-2011.) (Revised by NM, 9-Jan-2015.) |
Ref | Expression |
---|---|
mpbir3an.1 | |
mpbir3an.2 | |
mpbir3an.3 | |
mpbir3an.4 |
Ref | Expression |
---|---|
mpbir3an |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpbir3an.1 | . . 3 | |
2 | mpbir3an.2 | . . 3 | |
3 | mpbir3an.3 | . . 3 | |
4 | 1, 2, 3 | 3pm3.2i 1082 | . 2 |
5 | mpbir3an.4 | . 2 | |
6 | 4, 5 | mpbir 134 | 1 |
Colors of variables: wff set class |
Syntax hints: 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: limon 4239 limom 4336 issmo 5903 1eluzge0 8516 2eluzge0OLD 8518 2eluzge1 8519 0elunit 8854 1elunit 8855 4fvwrd4 8997 fzo0to42pr 9076 resqrexlemga 9621 |
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