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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 290 |
. 2
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7 | syl32anc.6 |
. 2
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8 | 1, 2, 3, 6, 7 | syl31anc 1138 |
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 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 df-3an 887 |
This theorem is referenced by: exple1 9310 leexp2rd 9410 |
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