Theorem pm5.33

Description: Theorem *5.33 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm5.33	⊢ ( ( 𝜑 ∧ ( 𝜓 → 𝜒 ) ) ↔ ( 𝜑 ∧ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ibar	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜑 ∧ 𝜓 ) ) )
2	1	imbi1d	⊢ ( 𝜑 → ( ( 𝜓 → 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) ) )
3	2	pm5.32i	⊢ ( ( 𝜑 ∧ ( 𝜓 → 𝜒 ) ) ↔ ( 𝜑 ∧ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) ) )