Theorem jca2r

Description: Inference conjoining the consequents of two implications. (Contributed by Rodolfo Medina, 17-Oct-2010)

	Ref	Expression
Hypotheses	jca2r.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	jca2r.2	⊢ ( 𝜓 → 𝜃 )
Assertion	jca2r	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 ∧ 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		jca2r.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		jca2r.2	⊢ ( 𝜓 → 𝜃 )
3	2	a1i	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
4	3 1	jcad	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 ∧ 𝜒 ) ) )