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	⊢ ( 𝑅1 ‘ ω ) ≈ ω

Proof

Step	Hyp	Ref	Expression
1		omina	⊢ ω ∈ Inacc
2		inar1	⊢ ( ω ∈ Inacc → ( 𝑅1 ‘ ω ) ≈ ω )
3	1 2	ax-mp	⊢ ( 𝑅1 ‘ ω ) ≈ ω