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Metamath Proof Explorer

Theorem ad2ant2r

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 8-Jan-2006)

		Ref	Expression
	Hypothesis	ad2ant2.1	$⊢ (φ \land ψ) \to χ$
	Assertion	ad2ant2r	$⊢ ((φ \land θ) \land (ψ \land τ)) \to χ$

Step	Hyp	Ref	Expression
1		ad2ant2.1	$⊢ (φ \land ψ) \to χ$
2	1	adantrr	$⊢ (φ \land (ψ \land τ)) \to χ$
3	2	adantlr	$⊢ ((φ \land θ) \land (ψ \land τ)) \to χ$