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| Mirrors > Home > HOLE Home > Th. List > ax-jca | GIF version | ||
| Description: Join common antecedents. (Contributed by Mario Carneiro, 8-Oct-2014.) |
| Ref | Expression |
|---|---|
| ax-jca.1 | ⊢ R⊧S |
| ax-jca.2 | ⊢ R⊧T |
| Ref | Expression |
|---|---|
| ax-jca | ⊢ R⊧(S, T) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | tr | . 2 term R | |
| 2 | ts | . . 3 term S | |
| 3 | tt | . . 3 term T | |
| 4 | 2, 3 | kct 10 | . 2 term (S, T) |
| 5 | 1, 4 | wffMMJ2 11 | 1 wff R⊧(S, T) |
| Colors of variables: type var term |
| This axiom is referenced by: jca 18 |
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