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Metamath Proof Explorer

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 ) ) )

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 ) ) )