Theorem pm5.4

Description: Antecedent absorption implication. Theorem *5.4 of WhiteheadRussell p. 125. (Contributed by NM, 5-Aug-1993)

	Ref	Expression
Assertion	pm5.4	⊢ ( ( 𝜑 → ( 𝜑 → 𝜓 ) ) ↔ ( 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.5	⊢ ( 𝜑 → ( ( 𝜑 → 𝜓 ) ↔ 𝜓 ) )
2	1	pm5.74i	⊢ ( ( 𝜑 → ( 𝜑 → 𝜓 ) ) ↔ ( 𝜑 → 𝜓 ) )