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Metamath Proof Explorer

Theorem 3ad2antr3

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 30-Dec-2007)

		Ref	Expression
	Hypothesis	3ad2antl.1	$⊢ (φ \land χ) \to θ$
	Assertion	3ad2antr3	$⊢ (φ \land (ψ \land τ \land χ)) \to θ$

Step	Hyp	Ref	Expression
1		3ad2antl.1	$⊢ (φ \land χ) \to θ$
2	1	adantrl	$⊢ (φ \land (τ \land χ)) \to θ$
3	2	3adantr1	$⊢ (φ \land (ψ \land τ \land χ)) \to θ$