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Mirrors > Home > ILE Home > Th. List > sbbidh | Unicode version |
Description: Deduction substituting both sides of a biconditional. New proofs should use sbbid 1819 instead. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.) |
Ref | Expression |
---|---|
sbbidh.1 |
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sbbidh.2 |
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Ref | Expression |
---|---|
sbbidh |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbbidh.1 |
. . 3
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2 | sbbidh.2 |
. . 3
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3 | 1, 2 | alrimih 1446 |
. 2
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4 | spsbbi 1817 |
. 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 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-ial 1515 |
This theorem depends on definitions: df-bi 116 df-sb 1737 |
This theorem is referenced by: sbcomxyyz 1946 |
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