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Metamath Proof Explorer

Theorem r1omALT

Description: Alternate proof of r1om , shorter as a consequence of inar1 , but requiring AC. (Contributed by Mario Carneiro, 27-May-2013) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	r1omALT	$⊢ R_{1} (ω) \approx ω$

Proof

Step	Hyp	Ref	Expression
1		omina	$⊢ ω \in Inacc$
2		inar1	$⊢ ω \in Inacc \to R_{1} (ω) \approx ω$
3	1 2	ax-mp	$⊢ R_{1} (ω) \approx ω$