Theorem brlmici

Description: Prove isomorphic by an explicit isomorphism. (Contributed by Stefan O'Rear, 25-Jan-2015)

	Ref	Expression
Assertion	brlmici	⊢ ( 𝐹 ∈ ( 𝑅 LMIso 𝑆 ) → 𝑅 ≃𝑚 𝑆 )

Proof

Step	Hyp	Ref	Expression
1		ne0i	⊢ ( 𝐹 ∈ ( 𝑅 LMIso 𝑆 ) → ( 𝑅 LMIso 𝑆 ) ≠ ∅ )
2		brlmic	⊢ ( 𝑅 ≃𝑚 𝑆 ↔ ( 𝑅 LMIso 𝑆 ) ≠ ∅ )
3	1 2	sylibr	⊢ ( 𝐹 ∈ ( 𝑅 LMIso 𝑆 ) → 𝑅 ≃𝑚 𝑆 )