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Mirrors > Home > ILE Home > Th. List > 4syl | GIF version |
Description: Inference chaining three syllogisms. The use of this theorem is marked "discouraged" because it can cause the "minimize" command to have very long run times. However, feel free to use "minimize 4syl /override" if you wish. (Contributed by BJ, 14-Jul-2018.) (New usage is discouraged.) |
Ref | Expression |
---|---|
4syl.1 | ⊢ (𝜑 → 𝜓) |
4syl.2 | ⊢ (𝜓 → 𝜒) |
4syl.3 | ⊢ (𝜒 → 𝜃) |
4syl.4 | ⊢ (𝜃 → 𝜏) |
Ref | Expression |
---|---|
4syl | ⊢ (𝜑 → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 4syl.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 4syl.2 | . . 3 ⊢ (𝜓 → 𝜒) | |
3 | 4syl.3 | . . 3 ⊢ (𝜒 → 𝜃) | |
4 | 1, 2, 3 | 3syl 17 | . 2 ⊢ (𝜑 → 𝜃) |
5 | 4syl.4 | . 2 ⊢ (𝜃 → 𝜏) | |
6 | 4, 5 | syl 14 | 1 ⊢ (𝜑 → 𝜏) |
Colors of variables: wff set class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 |
This theorem is referenced by: f1ocnvfvrneq 5442 fcof1o 5449 isoselem 5479 isose 5480 tposss 5884 smoiso 5940 fzssp1 9085 fzosplitsnm1 9218 fzofzp1 9236 fzostep1 9246 bcm1k 9687 climuni 10132 serif0 10189 |
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