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| Mirrors > Home > MPE Home > Th. List > jca31 | Structured version Visualization version GIF version | ||
| Description: Join three consequents. (Contributed by Jeff Hankins, 1-Aug-2009.) |
| Ref | Expression |
|---|---|
| jca31.1 | ⊢ (𝜑 → 𝜓) |
| jca31.2 | ⊢ (𝜑 → 𝜒) |
| jca31.3 | ⊢ (𝜑 → 𝜃) |
| Ref | Expression |
|---|---|
| jca31 | ⊢ (𝜑 → ((𝜓 ∧ 𝜒) ∧ 𝜃)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | jca31.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
| 2 | jca31.2 | . . 3 ⊢ (𝜑 → 𝜒) | |
| 3 | 1, 2 | jca 511 | . 2 ⊢ (𝜑 → (𝜓 ∧ 𝜒)) |
| 4 | jca31.3 | . 2 ⊢ (𝜑 → 𝜃) | |
| 5 | 3, 4 | jca 511 | 1 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) ∧ 𝜃)) |
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