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Mirrors > Home > HOLE Home > Th. List > simprd | GIF version |
Description: Extract an assumption from the context. (Contributed by Mario Carneiro, 8-Oct-2014.) |
Ref | Expression |
---|---|
simpld.1 | ⊢ R⊧(S, T) |
Ref | Expression |
---|---|
simprd | ⊢ R⊧T |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpld.1 | . 2 ⊢ R⊧(S, T) | |
2 | 1 | ax-cb2 30 | . . . 4 ⊢ (S, T):∗ |
3 | 2 | wctl 33 | . . 3 ⊢ S:∗ |
4 | 2 | wctr 34 | . . 3 ⊢ T:∗ |
5 | 3, 4 | simpr 23 | . 2 ⊢ (S, T)⊧T |
6 | 1, 5 | syl 16 | 1 ⊢ R⊧T |
Colors of variables: type var term |
Syntax hints: kct 10 ⊧wffMMJ2 11 |
This theorem was proved from axioms: ax-syl 15 ax-simpr 21 ax-cb2 30 ax-wctl 31 ax-wctr 32 |
This theorem is referenced by: mpd 156 exmid 199 ax2 204 |
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