Metamath Proof Explorer

Theorem ad3antlr

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

		Ref	Expression
	Hypothesis	ad2ant.1	$⊢ φ \to ψ$
	Assertion	ad3antlr	$⊢ (((χ \land φ) \land θ) \land τ) \to ψ$

Proof

Step	Hyp	Ref	Expression
1		ad2ant.1	$⊢ φ \to ψ$
2	1	adantl	$⊢ (χ \land φ) \to ψ$
3	2	ad2antrr	$⊢ (((χ \land φ) \land θ) \land τ) \to ψ$