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Metamath Proof Explorer

Theorem ibd

Description: Deduction that converts a biconditional implied by one of its arguments, into an implication. Deduction associated with ibi . (Contributed by NM, 26-Jun-2004)

		Ref	Expression
	Hypothesis	ibd.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜓 ↔ 𝜒 ) ) )
	Assertion	ibd	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		ibd.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜓 ↔ 𝜒 ) ) )
2		biimp	⊢ ( ( 𝜓 ↔ 𝜒 ) → ( 𝜓 → 𝜒 ) )
3	1 2	syli	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )