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Mirrors > Home > ILE Home > Th. List > 3impexpbicom | Unicode version |
Description: 3impexp 1378 with biconditional consequent of antecedent that is commuted in consequent. (Contributed by Alan Sare, 31-Dec-2011.) |
Ref | Expression |
---|---|
3impexpbicom |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bicom 139 |
. . . 4
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2 | imbi2 236 |
. . . . 5
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3 | 2 | biimpcd 158 |
. . . 4
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4 | 1, 3 | mpi 15 |
. . 3
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5 | 4 | 3expd 1167 |
. 2
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6 | 3impexp 1378 |
. . . 4
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7 | 6 | biimpri 132 |
. . 3
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8 | 7, 1 | syl6ibr 161 |
. 2
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9 | 5, 8 | impbii 125 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-3an 929 |
This theorem is referenced by: (None) |
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