Theorem jctild

Description: Deduction conjoining a theorem to left of consequent in an implication. (Contributed by NM, 21-Apr-2005)

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

Proof

Step	Hyp	Ref	Expression
1		jctild.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		jctild.2	⊢ ( 𝜑 → 𝜃 )
3	2	a1d	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
4	3 1	jcad	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 ∧ 𝜒 ) ) )