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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 ∈ V

Proof

Step	Hyp	Ref	Expression
1		nnexALT	⊢ ℕ ∈ V
2		qexALT	⊢ ℚ ∈ V
3	1 2	rpnnen1	⊢ ℝ ≼ ( ℚ ↑_m ℕ )
4		reldom	⊢ Rel ≼
5	4	brrelex1i	⊢ ( ℝ ≼ ( ℚ ↑_m ℕ ) → ℝ ∈ V )
6	3 5	ax-mp	⊢ ℝ ∈ V