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Metamath Proof Explorer

Theorem bi2.04

Description: Logical equivalence of commuted antecedents. Part of Theorem *4.87 of WhiteheadRussell p. 122. (Contributed by NM, 11-May-1993)

		Ref	Expression
	Assertion	bi2.04	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) ↔ ( 𝜓 → ( 𝜑 → 𝜒 ) ) )

Step	Hyp	Ref	Expression
1		pm2.04	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜓 → ( 𝜑 → 𝜒 ) ) )
2		pm2.04	⊢ ( ( 𝜓 → ( 𝜑 → 𝜒 ) ) → ( 𝜑 → ( 𝜓 → 𝜒 ) ) )
3	1 2	impbii	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) ↔ ( 𝜓 → ( 𝜑 → 𝜒 ) ) )