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Mirrors > Home > ILE Home > Th. List > syl311anc | 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 | |
syl311anc.6 |
Ref | Expression |
---|---|
syl311anc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylXanc.1 | . . 3 | |
2 | sylXanc.2 | . . 3 | |
3 | sylXanc.3 | . . 3 | |
4 | 1, 2, 3 | 3jca 1162 | . 2 |
5 | sylXanc.4 | . 2 | |
6 | sylXanc.5 | . 2 | |
7 | syl311anc.6 | . 2 | |
8 | 4, 5, 6, 7 | syl3anc 1220 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 w3a 963 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-3an 965 |
This theorem is referenced by: syl312anc 1241 syl321anc 1242 syl313anc 1244 syl331anc 1245 |
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