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Metamath Proof Explorer

Theorem 3anim3i

Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 19-Aug-2009)

		Ref	Expression
	Hypothesis	3animi.1	$⊢ φ \to ψ$
	Assertion	3anim3i	$⊢ (χ \land θ \land φ) \to (χ \land θ \land ψ)$

Step	Hyp	Ref	Expression
1		3animi.1	$⊢ φ \to ψ$
2		id	$⊢ χ \to χ$
3		id	$⊢ θ \to θ$
4	2 3 1	3anim123i	$⊢ (χ \land θ \land φ) \to (χ \land θ \land ψ)$