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Metamath Proof Explorer

Theorem biimp3a

Description: Infer implication from a logical equivalence. Similar to biimpa . (Contributed by NM, 4-Sep-2005)

		Ref	Expression
	Hypothesis	biimp3a.1	$⊢ (φ \land ψ) \to (χ \leftrightarrow θ)$
	Assertion	biimp3a	$⊢ (φ \land ψ \land χ) \to θ$

Step	Hyp	Ref	Expression
1		biimp3a.1	$⊢ (φ \land ψ) \to (χ \leftrightarrow θ)$
2	1	biimpa	$⊢ ((φ \land ψ) \land χ) \to θ$
3	2	3impa	$⊢ (φ \land ψ \land χ) \to θ$