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Mirrors > Home > ILE Home > Th. List > syl23anc | 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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syl23anc.6 |
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Ref | Expression |
---|---|
syl23anc |
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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 | 1, 2 | jca 306 |
. 2
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4 | sylXanc.3 |
. 2
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5 | sylXanc.4 |
. 2
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6 | sylXanc.5 |
. 2
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7 | syl23anc.6 |
. 2
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8 | 3, 4, 5, 6, 7 | syl13anc 1240 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 df-3an 980 |
This theorem is referenced by: div2subapd 8771 gcdaddm 11955 restopn2 13316 |
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