Theorem nfabd 2651

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 8-Oct-2016.)

Hypotheses

Ref	Expression
nfabd.1	|- F/ y ph
nfabd.2	|- ( ph -> F/ x ps )

Assertion

Ref	Expression
nfabd	|- ( ph -> F/_ x { y | ps } )

Proof of Theorem nfabd

Step	Hyp	Ref	Expression
1		nfabd.1	. 2 |- F/ y ph
2		nfabd.2	. . 3 |- ( ph -> F/ x ps )
3	2	adantr 465	. 2 |- ( ( ph /\ -. A. x x = y ) -> F/ x ps )
4	1, 3	nfabd2 2650	1 |- ( ph -> F/_ x { y | ps } )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1377   F/wnf 1599   {cab 2452   F/_wnfc 2615

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617

This theorem is referenced by:  nfsbcd  3357  nfcsb1d  3454  nfcsbd  3457  nfifd  3973  nfunid  4258  nfiotad  5560