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Metamath Proof Explorer

Theorem hmphsymb

Description: "Is homeomorphic to" is symmetric. (Contributed by FL, 22-Feb-2007)

		Ref	Expression
	Assertion	hmphsymb	⊢ ( 𝐽 ≃ 𝐾 ↔ 𝐾 ≃ 𝐽 )

Step	Hyp	Ref	Expression
1		hmphsym	⊢ ( 𝐽 ≃ 𝐾 → 𝐾 ≃ 𝐽 )
2		hmphsym	⊢ ( 𝐾 ≃ 𝐽 → 𝐽 ≃ 𝐾 )
3	1 2	impbii	⊢ ( 𝐽 ≃ 𝐾 ↔ 𝐾 ≃ 𝐽 )