Theorem pm3.45

Description: Theorem *3.45 (Fact) of WhiteheadRussell p. 113. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm3.45	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜑 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜓 ) )
2	1	anim1d	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜑 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜒 ) ) )