Theorem pm5.3

Description: Theorem *5.3 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005) (Proof shortened by Andrew Salmon, 7-May-2011)

	Ref	Expression
Assertion	pm5.3	⊢ ( ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜑 ∧ 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		simpl	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜑 )
2	1	biantrurd	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 ↔ ( 𝜑 ∧ 𝜒 ) ) )
3	2	pm5.74i	⊢ ( ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜑 ∧ 𝜒 ) ) )