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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 1159 | . 2 |
5 | mpbir3an.4 | . 2 | |
6 | 4, 5 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 w3a 962 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-3an 964 |
This theorem is referenced by: limon 4429 limom 4527 issmo 6185 xpider 6500 1eluzge0 9372 2eluzge1 9374 0elunit 9772 1elunit 9773 4fvwrd4 9920 fzo0to42pr 10000 resqrexlemga 10798 sincos1sgn 11474 sincos2sgn 11475 qnnen 11947 strleun 12051 sinhalfpilem 12875 sincos4thpi 12924 sincos6thpi 12926 pigt3 12928 |
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