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Mirrors > Home > ILE Home > Th. List > syl32anc | 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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sylXanc.5 |
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syl32anc.6 |
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Ref | Expression |
---|---|
syl32anc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylXanc.1 |
. 2
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2 | sylXanc.2 |
. 2
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3 | sylXanc.3 |
. 2
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4 | sylXanc.4 |
. . 3
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5 | sylXanc.5 |
. . 3
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6 | 4, 5 | jca 302 |
. 2
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7 | syl32anc.6 |
. 2
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8 | 1, 2, 3, 6, 7 | syl31anc 1187 |
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 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-3an 932 |
This theorem is referenced by: ioom 9879 modifeq2int 10000 modaddmodup 10001 seq3f1olemqsum 10114 seq3f1o 10118 exple1 10190 leexp2rd 10295 facubnd 10332 permnn 10358 dfabsmax 10829 expcnvre 11111 dvdsadd2b 11335 dvdsmulgcd 11506 sqgcd 11510 bezoutr 11513 cncongr2 11578 pw2dvds 11636 hashgcdlem 11695 tgioo 12465 |
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