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Mirrors > Home > ILE Home > Th. List > syl32anc | Unicode version |
Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.) |
Ref | Expression |
---|---|
sylXanc.1 | |
sylXanc.2 | |
sylXanc.3 | |
sylXanc.4 | |
sylXanc.5 | |
syl32anc.6 |
Ref | Expression |
---|---|
syl32anc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylXanc.1 | . 2 | |
2 | sylXanc.2 | . 2 | |
3 | sylXanc.3 | . 2 | |
4 | sylXanc.4 | . . 3 | |
5 | sylXanc.5 | . . 3 | |
6 | 4, 5 | jca 290 | . 2 |
7 | syl32anc.6 | . 2 | |
8 | 1, 2, 3, 6, 7 | syl31anc 1138 | 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: exple1 9310 leexp2rd 9410 |
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