Theorem cbv3h

Description: Rule used to change bound variables, using implicit substitution. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker cbv3hv if possible. (Contributed by NM, 8-Jun-1993) (Proof shortened by Andrew Salmon, 25-May-2011) (Proof shortened by Wolf Lammen, 12-May-2018) (New usage is discouraged.)

	Ref	Expression
Hypotheses	cbv3h.1	|- ( ph -> A. y ph )
	cbv3h.2	|- ( ps -> A. x ps )
	cbv3h.3	|- ( x = y -> ( ph -> ps ) )
Assertion	cbv3h	|- ( A. x ph -> A. y ps )

Proof

Step	Hyp	Ref	Expression
1		cbv3h.1	|- ( ph -> A. y ph )
2		cbv3h.2	|- ( ps -> A. x ps )
3		cbv3h.3	|- ( x = y -> ( ph -> ps ) )
4	1	nf5i	|- F/ y ph
5	2	nf5i	|- F/ x ps
6	4 5 3	cbv3	|- ( A. x ph -> A. y ps )