Metamath Proof Explorer

Theorem ad5ant125

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017) (Proof shortened by Wolf Lammen, 23-Jun-2022)

		Ref	Expression
	Hypothesis	ad5ant.1	$⊢ (φ \land ψ \land χ) \to θ$
	Assertion	ad5ant125	$⊢ ((((φ \land ψ) \land τ) \land η) \land χ) \to θ$

Step	Hyp	Ref	Expression
1		ad5ant.1	$⊢ (φ \land ψ \land χ) \to θ$
2	1	3expia	$⊢ (φ \land ψ) \to (χ \to θ)$
3	2	2a1d	$⊢ (φ \land ψ) \to (τ \to (η \to (χ \to θ)))$
4	3	imp41	$⊢ ((((φ \land ψ) \land τ) \land η) \land χ) \to θ$