Metamath Proof Explorer

Theorem simpr1l

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012) (Proof shortened by Wolf Lammen, 24-Jun-2022)

		Ref	Expression
	Assertion	simpr1l	$⊢ (τ \land ((φ \land ψ) \land χ \land θ)) \to φ$

Step	Hyp	Ref	Expression
1		simprl	$⊢ (τ \land (φ \land ψ)) \to φ$
2	1	3ad2antr1	$⊢ (τ \land ((φ \land ψ) \land χ \land θ)) \to φ$