Metamath Proof Explorer

Theorem simpr11

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

		Ref	Expression
	Assertion	simpr11	$⊢ (η \land ((φ \land ψ \land χ) \land θ \land τ)) \to φ$

Step	Hyp	Ref	Expression
1		simpr1	$⊢ (η \land (φ \land ψ \land χ)) \to φ$
2	1	3ad2antr1	$⊢ (η \land ((φ \land ψ \land χ) \land θ \land τ)) \to φ$