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Mirrors > Home > MPE Home > Th. List > syl231anc | 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 | |
syl33anc.6 | |
syl231anc.7 |
Ref | Expression |
---|---|
syl231anc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl12anc.1 | . . 3 | |
2 | syl12anc.2 | . . 3 | |
3 | 1, 2 | jca 554 | . 2 |
4 | syl12anc.3 | . 2 | |
5 | syl22anc.4 | . 2 | |
6 | syl23anc.5 | . 2 | |
7 | syl33anc.6 | . 2 | |
8 | syl231anc.7 | . 2 | |
9 | 3, 4, 5, 6, 7, 8 | syl131anc 1339 | 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: syl232anc 1353 isosctr 24551 axeuclid 25843 dalawlem3 35159 dalawlem6 35162 cdlemd7 35491 cdleme18c 35580 cdlemi 36108 cdlemk7 36136 cdlemk11 36137 cdlemk7u 36158 cdlemk11u 36159 cdlemk19xlem 36230 cdlemk55u1 36253 cdlemk56 36259 |
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