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Mirrors > Home > ILE Home > Th. List > syl121anc | 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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syl121anc.5 |
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Ref | Expression |
---|---|
syl121anc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylXanc.1 |
. 2
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2 | sylXanc.2 |
. . 3
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3 | sylXanc.3 |
. . 3
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4 | 2, 3 | jca 301 |
. 2
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5 | sylXanc.4 |
. 2
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6 | syl121anc.5 |
. 2
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7 | 1, 4, 5, 6 | syl3anc 1175 |
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 927 |
This theorem is referenced by: syl122anc 1184 tfisi 4417 tfrcllemsucfn 6134 sbthlemi6 6727 sbthlemi8 6729 div32apd 8344 div13apd 8345 expdivapd 10163 modfsummodlemstep 10914 |
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