Theorem nfsab 2345

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
nfsab.1	|- F/xph

Assertion

Ref	Expression
nfsab	|- F/x z e. {y | ph}

Distinct variable group:   x,z

Allowed substitution hints:   ph(x, y, z)

Proof of Theorem nfsab

Step	Hyp	Ref	Expression
1		nfsab.1	. . . 4 |- F/xph
2	1	nfri 1762	. . 3 |- (ph -> A.xph)
3	2	hbab 2344	. 2 |- (z e. {y | ph} -> A.x z e. {y | ph})
4	3	nfi 1551	1 |- F/x z e. {y | ph}

This proof depends on syntax axioms:   F/wnf 1544   e. wcel 1710  {cab 2339

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This proof depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340

This theorem is used by:  nfab  2494