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Mirrors > Home > MPE Home > Th. List > syl212anc | Structured version Visualization version Unicode version |
Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.) |
Ref | Expression |
---|---|
syl12anc.1 | |
syl12anc.2 | |
syl12anc.3 | |
syl22anc.4 | |
syl23anc.5 | |
syl212anc.6 |
Ref | Expression |
---|---|
syl212anc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl12anc.1 | . 2 | |
2 | syl12anc.2 | . 2 | |
3 | syl12anc.3 | . 2 | |
4 | syl22anc.4 | . . 3 | |
5 | syl23anc.5 | . . 3 | |
6 | 4, 5 | jca 554 | . 2 |
7 | syl212anc.6 | . 2 | |
8 | 1, 2, 3, 6, 7 | syl211anc 1332 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 |
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 197 df-an 386 df-3an 1039 |
This theorem is referenced by: pntrmax 25253 tglineineq 25538 tglineinteq 25540 paddasslem4 35109 4atexlemu 35350 4atexlemv 35351 cdleme20aN 35597 cdleme20g 35603 cdlemg9a 35920 cdlemg12a 35931 cdlemg17dALTN 35952 cdlemg18b 35967 cdlemg18c 35968 |
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