Metamath Proof Explorer

Theorem 4animp1

Description: A single hypothesis unification deduction with an assertion which is an implication with a 4-right-nested conjunction antecedent. (Contributed by Alan Sare, 30-May-2018)

		Ref	Expression
	Hypothesis	4animp1.1	$⊢ (φ \land ψ \land χ) \to (τ \leftrightarrow θ)$
	Assertion	4animp1	$⊢ (((φ \land ψ) \land χ) \land θ) \to τ$

Proof

Step	Hyp	Ref	Expression
1		4animp1.1	$⊢ (φ \land ψ \land χ) \to (τ \leftrightarrow θ)$
2		simpr	$⊢ (((φ \land ψ) \land χ) \land θ) \to θ$
3	1	ad4ant123	$⊢ (((φ \land ψ) \land χ) \land θ) \to (τ \leftrightarrow θ)$
4	2 3	mpbird	$⊢ (((φ \land ψ) \land χ) \land θ) \to τ$