Theorem 3com12d

Description: Commutation in consequent. Swap 1st and 2nd. (Contributed by Jeff Hankins, 17-Nov-2009)

	Ref	Expression
Hypothesis	3com12d.1	⊢ ( 𝜑 → ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) )
Assertion	3com12d	⊢ ( 𝜑 → ( 𝜒 ∧ 𝜓 ∧ 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		3com12d.1	⊢ ( 𝜑 → ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) )
2		id	⊢ ( ( 𝜒 ∧ 𝜓 ∧ 𝜃 ) → ( 𝜒 ∧ 𝜓 ∧ 𝜃 ) )
3	2	3com12	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → ( 𝜒 ∧ 𝜓 ∧ 𝜃 ) )
4	1 3	syl	⊢ ( 𝜑 → ( 𝜒 ∧ 𝜓 ∧ 𝜃 ) )