Theorem jca32

Description: Join three consequents. (Contributed by FL, 1-Aug-2009)

	Ref	Expression
Hypotheses	jca31.1	⊢ ( 𝜑 → 𝜓 )
	jca31.2	⊢ ( 𝜑 → 𝜒 )
	jca31.3	⊢ ( 𝜑 → 𝜃 )
Assertion	jca32	⊢ ( 𝜑 → ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		jca31.1	⊢ ( 𝜑 → 𝜓 )
2		jca31.2	⊢ ( 𝜑 → 𝜒 )
3		jca31.3	⊢ ( 𝜑 → 𝜃 )
4	2 3	jca	⊢ ( 𝜑 → ( 𝜒 ∧ 𝜃 ) )
5	1 4	jca	⊢ ( 𝜑 → ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) )