Theorem pm5.501

Description: Theorem *5.501 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm5.501	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜑 ↔ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.1im	⊢ ( 𝜑 → ( 𝜓 → ( 𝜑 ↔ 𝜓 ) ) )
2		biimp	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜑 → 𝜓 ) )
3	2	com12	⊢ ( 𝜑 → ( ( 𝜑 ↔ 𝜓 ) → 𝜓 ) )
4	1 3	impbid	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜑 ↔ 𝜓 ) ) )