Description: Inference conjoining a theorem to right of consequent in an implication. (Contributed by NM, 31-Dec-1993)
Ref | Expression | ||
---|---|---|---|
Hypotheses | jctil.1 | ⊢ ( 𝜑 → 𝜓 ) | |
jctil.2 | ⊢ 𝜒 | ||
Assertion | jctir | ⊢ ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | jctil.1 | ⊢ ( 𝜑 → 𝜓 ) | |
2 | jctil.2 | ⊢ 𝜒 | |
3 | 2 | a1i | ⊢ ( 𝜑 → 𝜒 ) |
4 | 1 3 | jca | ⊢ ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) |