Theorem csbnestg

Description: Nest the composition of two substitutions. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker csbnestgw when possible. (Contributed by NM, 23-Nov-2005) (Proof shortened by Mario Carneiro, 10-Nov-2016) (New usage is discouraged.)

	Ref	Expression
Assertion	csbnestg	|- ( A e. V -> [_ A / x ]_ [_ B / y ]_ C = [_ [_ A / x ]_ B / y ]_ C )

Proof

Step	Hyp	Ref	Expression
1		nfcv	|- F/_ x C
2	1	ax-gen	|- A. y F/_ x C
3		csbnestgf	|- ( ( A e. V /\ A. y F/_ x C ) -> [_ A / x ]_ [_ B / y ]_ C = [_ [_ A / x ]_ B / y ]_ C )
4	2 3	mpan2	|- ( A e. V -> [_ A / x ]_ [_ B / y ]_ C = [_ [_ A / x ]_ B / y ]_ C )