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Mirrors > Home > ILE Home > Th. List > imbibi | Unicode version |
Description: The antecedent of one side of a biconditional can be moved out of the biconditional to become the antecedent of the remaining biconditional. (Contributed by BJ, 1-Jan-2025.) (Proof shortened by Wolf Lammen, 5-Jan-2025.) |
Ref | Expression |
---|---|
imbibi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.4 249 |
. . 3
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2 | imbi2 237 |
. . 3
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3 | 1, 2 | bitr3id 194 |
. 2
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4 | 3 | pm5.74rd 183 |
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 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: snssg 3725 |
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