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Mirrors > Home > ILE Home > Th. List > syl31anc | Unicode version |
Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.) |
Ref | Expression |
---|---|
sylXanc.1 |
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sylXanc.2 |
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sylXanc.3 |
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sylXanc.4 |
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syl31anc.5 |
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Ref | Expression |
---|---|
syl31anc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylXanc.1 |
. . 3
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2 | sylXanc.2 |
. . 3
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3 | sylXanc.3 |
. . 3
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4 | 1, 2, 3 | 3jca 1121 |
. 2
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5 | sylXanc.4 |
. 2
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6 | syl31anc.5 |
. 2
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7 | 4, 5, 6 | syl2anc 403 |
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 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 df-3an 924 |
This theorem is referenced by: syl32anc 1180 stoic4b 1365 enq0tr 6914 ltmul12a 8233 lt2msq1 8258 ledivp1 8276 lemul1ad 8312 lemul2ad 8313 lediv2ad 9105 difelfznle 9451 expubnd 9863 expcanlem 9973 expcand 9975 dvdsadd 10633 divalgmod 10721 gcdzeq 10805 rplpwr 10810 sqgcd 10812 bezoutr 10815 rpmulgcd2 10871 rpdvds 10875 divgcdodd 10916 oddpwdclemxy 10941 divnumden 10968 crth 10994 phimullem 10995 |
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