Theorem mapco2

Description: Post-composition (renaming indices) of a mapping viewed as a point. (Contributed by Stefan O'Rear, 5-Oct-2014) (Revised by Stefan O'Rear, 5-May-2015)

	Ref	Expression
Hypothesis	mapco2.3	|- E e. _V
Assertion	mapco2	|- ( ( A e. ( B ^m C ) /\ D : E --> C ) -> ( A o. D ) e. ( B ^m E ) )

Proof

Step	Hyp	Ref	Expression
1		mapco2.3	|- E e. _V
2		mapco2g	|- ( ( E e. _V /\ A e. ( B ^m C ) /\ D : E --> C ) -> ( A o. D ) e. ( B ^m E ) )
3	1 2	mp3an1	|- ( ( A e. ( B ^m C ) /\ D : E --> C ) -> ( A o. D ) e. ( B ^m E ) )