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Mirrors > Home > NFE Home > Th. List > syl12anc | Unicode version |
Description: Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.) |
Ref | Expression |
---|---|
sylXanc.1 |
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sylXanc.2 |
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sylXanc.3 |
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syl12anc.4 |
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Ref | Expression |
---|---|
syl12anc |
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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 | jca32 521 |
. 2
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5 | syl12anc.4 |
. 2
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6 | 4, 5 | syl 15 |
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 |
This theorem is referenced by: syl22anc 1183 raaan 3658 raaanv 3659 nndisjeq 4430 prepeano4 4452 ssfin 4471 ncfinraise 4482 ncfinlower 4484 nnpweq 4524 peano4 4558 f1oiso2 5501 frecsuc 6323 |
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