Metamath Proof Explorer

Theorem ad7antr

Description: Deduction adding 7 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017) (Proof shortened by Wolf Lammen, 5-Apr-2022)

		Ref	Expression
	Hypothesis	ad2ant.1	$⊢ φ \to ψ$
	Assertion	ad7antr	$⊢ (((((((φ \land χ) \land θ) \land τ) \land η) \land ζ) \land σ) \land ρ) \to ψ$

Step	Hyp	Ref	Expression
1		ad2ant.1	$⊢ φ \to ψ$
2	1	adantr	$⊢ (φ \land χ) \to ψ$
3	2	ad6antr	$⊢ (((((((φ \land χ) \land θ) \land τ) \land η) \land ζ) \land σ) \land ρ) \to ψ$