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Mirrors > Home > ILE Home > Th. List > 3impexpbicom | Unicode version |
Description: 3impexp 1366 with biconditional consequent of antecedent that is commuted in consequent. (Contributed by Alan Sare, 31-Dec-2011.) |
Ref | Expression |
---|---|
3impexpbicom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bicom 138 | . . . 4 | |
2 | imbi2 235 | . . . . 5 | |
3 | 2 | biimpcd 157 | . . . 4 |
4 | 1, 3 | mpi 15 | . . 3 |
5 | 4 | 3expd 1155 | . 2 |
6 | 3impexp 1366 | . . . 4 | |
7 | 6 | biimpri 131 | . . 3 |
8 | 7, 1 | syl6ibr 160 | . 2 |
9 | 5, 8 | impbii 124 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 w3a 919 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 df-3an 921 |
This theorem is referenced by: (None) |
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