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Mirrors > Home > NFE Home > Th. List > syl113anc | 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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syl113anc.6 |
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Ref | Expression |
---|---|
syl113anc |
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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 |
. . 3
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4 | sylXanc.4 |
. . 3
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5 | sylXanc.5 |
. . 3
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6 | 3, 4, 5 | 3jca 1132 |
. 2
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7 | syl113anc.6 |
. 2
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8 | 1, 2, 6, 7 | syl3anc 1182 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 177 df-an 360 df-3an 936 |
This theorem is referenced by: syl123anc 1199 syl213anc 1201 |
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