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Metamath Proof Explorer

Theorem jctr

Description: Inference conjoining a theorem to the right of a consequent. (Contributed by NM, 18-Aug-1993) (Proof shortened by Wolf Lammen, 24-Oct-2012)

		Ref	Expression
	Hypothesis	jctl.1	$⊢ ψ$
	Assertion	jctr	$⊢ φ \to (φ \land ψ)$

Proof

Step	Hyp	Ref	Expression
1		jctl.1	$⊢ ψ$
2		id	$⊢ φ \to φ$
3	2 1	jctir	$⊢ φ \to (φ \land ψ)$