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Mirrors > Home > MPE Home > Th. List > Mathboxes > 3impexpbicom | Structured version Visualization version Unicode version |
Description: Version of 3impexp 1289 where in addition the consequent is commuted. (Contributed by Alan Sare, 31-Dec-2011.) |
Ref | Expression |
---|---|
3impexpbicom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bicom 212 | . . . 4 | |
2 | imbi2 338 | . . . . 5 | |
3 | 2 | biimpcd 239 | . . . 4 |
4 | 1, 3 | mpi 20 | . . 3 |
5 | 4 | 3expd 1284 | . 2 |
6 | 3impexp 1289 | . . . 4 | |
7 | 6 | biimpri 218 | . . 3 |
8 | 7, 1 | syl6ibr 242 | . 2 |
9 | 5, 8 | impbii 199 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 w3a 1037 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-an 386 df-3an 1039 |
This theorem is referenced by: 3impexpbicomiVD 39093 |
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