Theorem nfaov 41259

Description: Bound-variable hypothesis builder for operation value, analogous to nfov 6676. To prove a deduction version of this analogous to nfovd 6675 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 41216). (Contributed by Alexander van der Vekens, 26-May-2017.)

Hypotheses

Ref	Expression
nfaov.2	|- F/_ x A
nfaov.3	|- F/_ x F
nfaov.4	|- F/_ x B

Assertion

Ref	Expression
nfaov	|- F/_ x (( A F B))

Proof of Theorem nfaov

Step	Hyp	Ref	Expression
1		df-aov 41198	. 2 |- (( A F B)) = ( F''' <. A , B >. )
2		nfaov.3	. . 3 |- F/_ x F
3		nfaov.2	. . . 4 |- F/_ x A
4		nfaov.4	. . . 4 |- F/_ x B
5	3, 4	nfop 4418	. . 3 |- F/_ x <. A , B >.
6	2, 5	nfafv 41216	. 2 |- F/_ x ( F''' <. A , B >. )
7	1, 6	nfcxfr 2762	1 |- F/_ x (( A F B))

Syntax hints:   F/_wnfc 2751   <.cop 4183  '''cafv 41194   ((caov 41195

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ral 2917  df-rex 2918  df-rab 2921  df-v 3202  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-if 4087  df-sn 4178  df-pr 4180  df-op 4184  df-uni 4437  df-br 4654  df-opab 4713  df-xp 5120  df-rel 5121  df-cnv 5122  df-co 5123  df-dm 5124  df-res 5126  df-iota 5851  df-fun 5890  df-fv 5896  df-dfat 41196  df-afv 41197  df-aov 41198

This theorem is referenced by:  csbaovg  41260