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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-syl66ib | Structured version Visualization version GIF version |
Description: A mixed syllogism inference derived from syl6ib 250. In addition to bj-dvelimdv1 35032, it can also shorten alexsubALTlem4 23199 (4821>4812), supsrlem 10868 (2868>2863). (Contributed by BJ, 20-Oct-2021.) |
Ref | Expression |
---|---|
bj-syl66ib.1 | ⊢ (𝜑 → (𝜓 → 𝜃)) |
bj-syl66ib.2 | ⊢ (𝜃 → 𝜏) |
bj-syl66ib.3 | ⊢ (𝜏 ↔ 𝜒) |
Ref | Expression |
---|---|
bj-syl66ib | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-syl66ib.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜃)) | |
2 | bj-syl66ib.2 | . . 3 ⊢ (𝜃 → 𝜏) | |
3 | 1, 2 | syl6 35 | . 2 ⊢ (𝜑 → (𝜓 → 𝜏)) |
4 | bj-syl66ib.3 | . 2 ⊢ (𝜏 ↔ 𝜒) | |
5 | 3, 4 | syl6ib 250 | 1 ⊢ (𝜑 → (𝜓 → 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 |
This theorem is referenced by: bj-dvelimdv1 35032 |
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