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| Mirrors > Home > MPE Home > Th. List > jctir | Structured version Visualization version GIF version | ||
| Description: Inference conjoining a theorem to right of consequent in an implication. (Contributed by NM, 31-Dec-1993.) |
| Ref | Expression |
|---|---|
| jctil.1 | ⊢ (𝜑 → 𝜓) |
| jctil.2 | ⊢ 𝜒 |
| Ref | Expression |
|---|---|
| jctir | ⊢ (𝜑 → (𝜓 ∧ 𝜒)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | jctil.1 | . 2 ⊢ (𝜑 → 𝜓) | |
| 2 | jctil.2 | . . 3 ⊢ 𝜒 | |
| 3 | 2 | a1i 11 | . 2 ⊢ (𝜑 → 𝜒) |
| 4 | 1, 3 | jca 511 | 1 ⊢ (𝜑 → (𝜓 ∧ 𝜒)) |
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