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Mirrors > Home > ILE Home > Th. List > syl7 | Unicode version |
Description: A syllogism rule of inference. The second premise is used to replace the third antecedent of the first premise. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 3-Aug-2012.) |
Ref | Expression |
---|---|
syl7.1 |
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syl7.2 |
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Ref | Expression |
---|---|
syl7 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl7.1 |
. . 3
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2 | 1 | a1i 9 |
. 2
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3 | syl7.2 |
. 2
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4 | 2, 3 | syl5d 68 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 |
This theorem is referenced by: syl7bi 164 syl3an3 1216 fvmptt 5430 nneneq 6653 pr2nelem 6916 ndvdssub 11373 |
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