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Mirrors > Home > ILE Home > Th. List > syl31anc | Unicode version |
Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.) |
Ref | Expression |
---|---|
sylXanc.1 | |
sylXanc.2 | |
sylXanc.3 | |
sylXanc.4 | |
syl31anc.5 |
Ref | Expression |
---|---|
syl31anc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylXanc.1 | . . 3 | |
2 | sylXanc.2 | . . 3 | |
3 | sylXanc.3 | . . 3 | |
4 | 1, 2, 3 | 3jca 1084 | . 2 |
5 | sylXanc.4 | . 2 | |
6 | syl31anc.5 | . 2 | |
7 | 4, 5, 6 | syl2anc 391 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 w3a 885 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 df-3an 887 |
This theorem is referenced by: syl32anc 1143 stoic4b 1322 enq0tr 6532 ltmul12a 7826 lt2msq1 7851 ledivp1 7869 lemul1ad 7905 lemul2ad 7906 lediv2ad 8645 difelfznle 8993 expubnd 9311 |
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