Theorem nfabd 2623

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 471	. 2 |- ( ( ph /\ -. A. x x = y ) -> F/ x ps )
4	1, 3	nfabd2 2622	1 |- ( ph -> F/_ x { y | ps } )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1453   F/wnf 1678   {cab 2448   F/_wnfc 2590

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-10 1926  ax-11 1931  ax-12 1944  ax-13 2102  ax-ext 2442

This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1675  df-nf 1679  df-sb 1809  df-clab 2449  df-cleq 2455  df-clel 2458  df-nfc 2592

This theorem is referenced by:  nfsbcd  3300  nfcsb1d  3389  nfcsbd  3392  nfifd  3921  nfunid  4219  nfiotad  5568