Theorem lmimf1o

Description: An isomorphism of left modules is a bijection. (Contributed by Stefan O'Rear, 21-Jan-2015)

	Ref	Expression
Hypotheses	islmim.b	|- B = ( Base ` R )
	islmim.c	|- C = ( Base ` S )
Assertion	lmimf1o	|- ( F e. ( R LMIso S ) -> F : B -1-1-onto-> C )

Proof

Step	Hyp	Ref	Expression
1		islmim.b	|- B = ( Base ` R )
2		islmim.c	|- C = ( Base ` S )
3	1 2	islmim	|- ( F e. ( R LMIso S ) <-> ( F e. ( R LMHom S ) /\ F : B -1-1-onto-> C ) )
4	3	simprbi	|- ( F e. ( R LMIso S ) -> F : B -1-1-onto-> C )