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Metamath Proof Explorer

Theorem reexALT

Description: Alternate proof of reex . (Contributed by NM, 30-Jul-2004) (Revised by Mario Carneiro, 23-Aug-2014) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	reexALT	$⊢ ℝ \in V$

Proof

Step	Hyp	Ref	Expression
1		nnexALT	$⊢ ℕ \in V$
2		qexALT	$⊢ ℚ \in V$
3	1 2	rpnnen1	$⊢ ℝ ≼ (ℚ^{ℕ})$
4		reldom	$⊢ Rel ≼$
5	4	brrelex1i	$⊢ ℝ ≼ (ℚ^{ℕ}) \to ℝ \in V$
6	3 5	ax-mp	$⊢ ℝ \in V$