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Mirrors > Home > ILE Home > Th. List > sbbid | Unicode version |
Description: Deduction substituting both sides of a biconditional. (Contributed by NM, 30-Jun-1993.) |
Ref | Expression |
---|---|
sbbid.1 |
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sbbid.2 |
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Ref | Expression |
---|---|
sbbid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbbid.1 |
. . 3
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2 | sbbid.2 |
. . 3
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3 | 1, 2 | alrimi 1533 |
. 2
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4 | spsbbi 1855 |
. 2
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5 | 3, 4 | syl 14 |
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-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-4 1521 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 |
This theorem is referenced by: bezoutlemmain 12122 |
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