Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > syl312anc | Unicode version |
Description: Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.) |
Ref | Expression |
---|---|
sylXanc.1 | |
sylXanc.2 | |
sylXanc.3 | |
sylXanc.4 | |
sylXanc.5 | |
sylXanc.6 | |
syl312anc.7 |
Ref | Expression |
---|---|
syl312anc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylXanc.1 | . 2 | |
2 | sylXanc.2 | . 2 | |
3 | sylXanc.3 | . 2 | |
4 | sylXanc.4 | . 2 | |
5 | sylXanc.5 | . . 3 | |
6 | sylXanc.6 | . . 3 | |
7 | 5, 6 | jca 304 | . 2 |
8 | syl312anc.7 | . 2 | |
9 | 1, 2, 3, 4, 7, 8 | syl311anc 1241 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 967 |
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 969 |
This theorem is referenced by: pythagtriplem19 12203 |
Copyright terms: Public domain | W3C validator |