Theorem idcncfg

Description: The identity function is a continuous function on CC . (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Hypotheses	idcncfg.a	|- ( ph -> A C_ B )
	idcncfg.b	|- ( ph -> B C_ CC )
Assertion	idcncfg	|- ( ph -> ( x e. A |-> x ) e. ( A -cn-> B ) )

Proof

Step	Hyp	Ref	Expression
1		idcncfg.a	|- ( ph -> A C_ B )
2		idcncfg.b	|- ( ph -> B C_ CC )
3		cncfmptid	|- ( ( A C_ B /\ B C_ CC ) -> ( x e. A |-> x ) e. ( A -cn-> B ) )
4	1 2 3	syl2anc	|- ( ph -> ( x e. A |-> x ) e. ( A -cn-> B ) )