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Metamath Proof Explorer

Theorem 3anim1i

Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 16-Aug-2009)

		Ref	Expression
	Hypothesis	3animi.1	$⊢ φ \to ψ$
	Assertion	3anim1i	$⊢ (φ \land χ \land θ) \to (ψ \land χ \land θ)$

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