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Mirrors > Home > ILE Home > Th. List > biimp3ar | Unicode version |
Description: Infer implication from a logical equivalence. Similar to biimpar 297. (Contributed by NM, 2-Jan-2009.) |
Ref | Expression |
---|---|
biimp3a.1 |
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Ref | Expression |
---|---|
biimp3ar |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biimp3a.1 |
. . 3
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2 | 1 | exbiri 382 |
. 2
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3 | 2 | 3imp 1193 |
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 df-3an 980 |
This theorem is referenced by: rmoi 3056 brelrng 4858 ssfzo12 10221 abssubge0 11106 qredeu 12091 basgen2 13512 logbprmirr 14321 lgssq 14372 lgssq2 14373 |
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