Theorem jctird

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

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

Proof

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