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Mirrors > Home > MPE Home > Th. List > jctil | Structured version Visualization version GIF version |
Description: Inference conjoining a theorem to left of consequent in an implication. (Contributed by NM, 31-Dec-1993.) |
Ref | Expression |
---|---|
jctil.1 | ⊢ (𝜑 → 𝜓) |
jctil.2 | ⊢ 𝜒 |
Ref | Expression |
---|---|
jctil | ⊢ (𝜑 → (𝜒 ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | jctil.2 | . . 3 ⊢ 𝜒 | |
2 | 1 | a1i 11 | . 2 ⊢ (𝜑 → 𝜒) |
3 | jctil.1 | . 2 ⊢ (𝜑 → 𝜓) | |
4 | 2, 3 | jca 512 | 1 ⊢ (𝜑 → (𝜒 ∧ 𝜓)) |
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