Theorem nfoprab3 5549

Description: The abstraction variables in an operation class abstraction are not free. (Contributed by NM, 22-Aug-2013.)

Assertion

Ref	Expression
nfoprab3	|- F/_z{<.<.x, y>., z>. | ph}

Proof of Theorem nfoprab3

Dummy variable w is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-oprab 5529	. 2 |- {<.<.x, y>., z>. | ph} = {w | E.xE.yE.z(w = <.<.x, y>., z>. /\ ph)}
2		nfe1 1732	. . . . 5 |- F/zE.z(w = <.<.x, y>., z>. /\ ph)
3	2	nfex 1843	. . . 4 |- F/zE.yE.z(w = <.<.x, y>., z>. /\ ph)
4	3	nfex 1843	. . 3 |- F/zE.xE.yE.z(w = <.<.x, y>., z>. /\ ph)
5	4	nfab 2494	. 2 |- F/_z{w | E.xE.yE.z(w = <.<.x, y>., z>. /\ ph)}
6	1, 5	nfcxfr 2487	1 |- F/_z{<.<.x, y>., z>. | ph}

Syntax hints:   /\ wa 358  E.wex 1541   = wceq 1642  {cab 2339   F/_wnfc 2477  <.cop 4562  {coprab 5528

This theorem was proved from 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  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-oprab 5529

This theorem is referenced by:  ov3  5600