Theorem nfabd 2613

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 466	. 2 |- ( ( ph /\ -. A. x x = y ) -> F/ x ps )
4	1, 3	nfabd2 2612	1 |- ( ph -> F/_ x { y | ps } )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1435   F/wnf 1663   {cab 2414   F/_wnfc 2577

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407

This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579

This theorem is referenced by:  nfsbcd  3326  nfcsb1d  3415  nfcsbd  3418  nfifd  3943  nfunid  4229  nfiotad  5568