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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdbi | Unicode version |
Description: A biconditional between two bounded formulas is bounded. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdbi.1 |
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bdbi.2 |
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Ref | Expression |
---|---|
bdbi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdbi.1 |
. . . 4
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2 | bdbi.2 |
. . . 4
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3 | 1, 2 | ax-bdim 14486 |
. . 3
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4 | 2, 1 | ax-bdim 14486 |
. . 3
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5 | 3, 4 | ax-bdan 14487 |
. 2
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6 | dfbi2 388 |
. 2
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7 | 5, 6 | bd0r 14497 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-bd0 14485 ax-bdim 14486 ax-bdan 14487 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: (None) |
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