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Mirrors > Home > ILE Home > Th. List > syl3anb | Unicode version |
Description: A triple syllogism inference. (Contributed by NM, 15-Oct-2005.) |
Ref | Expression |
---|---|
syl3anb.1 |
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syl3anb.2 |
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syl3anb.3 |
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syl3anb.4 |
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Ref | Expression |
---|---|
syl3anb |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl3anb.1 |
. . 3
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2 | syl3anb.2 |
. . 3
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3 | syl3anb.3 |
. . 3
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4 | 1, 2, 3 | 3anbi123i 1188 |
. 2
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5 | syl3anb.4 |
. 2
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6 | 4, 5 | sylbi 121 |
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: syl3anbr 1282 poxp 6226 |
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