Theorem pm5.31

Description: Theorem *5.31 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm5.31	⊢ ( ( 𝜒 ∧ ( 𝜑 → 𝜓 ) ) → ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		simpr	⊢ ( ( 𝜒 ∧ ( 𝜑 → 𝜓 ) ) → ( 𝜑 → 𝜓 ) )
2		simpl	⊢ ( ( 𝜒 ∧ ( 𝜑 → 𝜓 ) ) → 𝜒 )
3	1 2	jctird	⊢ ( ( 𝜒 ∧ ( 𝜑 → 𝜓 ) ) → ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) )