Theorem pm4.45im

Description: Conjunction with implication. Compare Theorem *4.45 of WhiteheadRussell p. 119. (Contributed by NM, 17-May-1998)

	Ref	Expression
Assertion	pm4.45im	⊢ ( 𝜑 ↔ ( 𝜑 ∧ ( 𝜓 → 𝜑 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ax-1	⊢ ( 𝜑 → ( 𝜓 → 𝜑 ) )
2	1	pm4.71i	⊢ ( 𝜑 ↔ ( 𝜑 ∧ ( 𝜓 → 𝜑 ) ) )