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 ) )