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Mirrors > Home > ILE Home > Th. List > syl33anc | 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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sylXanc.6 |
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syl33anc.7 |
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Ref | Expression |
---|---|
syl33anc |
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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 1129 |
. 2
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5 | sylXanc.4 |
. 2
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6 | sylXanc.5 |
. 2
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7 | sylXanc.6 |
. 2
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8 | syl33anc.7 |
. 2
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9 | 4, 5, 6, 7, 8 | syl13anc 1186 |
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: strleund 11829 iscnp4 12168 cnpnei 12169 cnptopco 12172 cncnp 12180 cnptopresti 12188 lmtopcnp 12200 txcnp 12221 xmetrtri 12304 bl2in 12331 blhalf 12336 blssps 12355 blss 12356 |
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