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Metamath Proof Explorer

Theorem ancrd

Description: Deduction conjoining antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994) (Proof shortened by Wolf Lammen, 1-Nov-2012)

		Ref	Expression
	Hypothesis	ancrd.1	$⊢ φ \to (ψ \to χ)$
	Assertion	ancrd	$⊢ φ \to (ψ \to (χ \land ψ))$

Proof

Step	Hyp	Ref	Expression
1		ancrd.1	$⊢ φ \to (ψ \to χ)$
2		idd	$⊢ φ \to (ψ \to ψ)$
3	1 2	jcad	$⊢ φ \to (ψ \to (χ \land ψ))$