Metamath Proof Explorer


Theorem jctil

Description: Inference conjoining a theorem to left of consequent in an implication. (Contributed by NM, 31-Dec-1993)

Ref Expression
Hypotheses jctil.1 ⊢ ( 𝜑 → 𝜓 )
jctil.2 ⊢ 𝜒
Assertion jctil ( 𝜑 → ( 𝜒 ∧ 𝜓 ) )

Proof

Step Hyp Ref Expression
1 jctil.1 ⊢ ( 𝜑 → 𝜓 )
2 jctil.2 ⊢ 𝜒
3 2 a1i ⊢ ( 𝜑 → 𝜒 )
4 3 1 jca ⊢ ( 𝜑 → ( 𝜒 ∧ 𝜓 ) )