Theorem nfaov

Description: Bound-variable hypothesis builder for operation value, analogous to nfov . To prove a deduction version of this analogous to nfovd is not quickly possible because many deduction versions for bound-variable hypothesis builder for constructs the definition of alternative operation values is based on are not available (see nfafv ). (Contributed by Alexander van der Vekens, 26-May-2017)

	Ref	Expression
Hypotheses	nfaov.2	|- F/_ x A
	nfaov.3	|- F/_ x F
	nfaov.4	|- F/_ x B
Assertion	nfaov	|- F/_ x (( A F B ))

Proof

Step	Hyp	Ref	Expression
1		nfaov.2	|- F/_ x A
2		nfaov.3	|- F/_ x F
3		nfaov.4	|- F/_ x B
4		df-aov	|- (( A F B )) = ( F ''' <. A , B >. )
5	1 3	nfop	|- F/_ x <. A , B >.
6	2 5	nfafv	|- F/_ x ( F ''' <. A , B >. )
7	4 6	nfcxfr	|- F/_ x (( A F B ))