Theorem hbrab1 1775

Description: The abstraction variable in a restricted class abstraction isn't free.

Assertion

Ref	Expression
hbrab1	|- (y e. {x e. A | ph} -> A.x y e. {x e. A | ph})

Distinct variable group:   x,y

Proof of Theorem hbrab1

Step	Hyp	Ref	Expression
1		df-rab 1655	. 2 |- {x e. A | ph} = {x | (x e. A /\ ph)}
2		hbab1 1469	. 2 |- (y e. {x | (x e. A /\ ph)} -> A.x y e. {x | (x e. A /\ ph)})
3	1, 2	hbxfr 1566	1 |- (y e. {x e. A | ph} -> A.x y e. {x e. A | ph})

Syntax hints:   -> wi 3   /\ wa 223  A.wal 956   e. wcel 960  {cab 1466  {crab 1651

This theorem is referenced by:  reuuni2f 2889  reuuni4 2893  reuuniss 2895  reuuniss2 2897  reusn 2898  rabxfr 2908  reuunixfr 2912  onminsb 3015  oawordeulem 4194  tz9.12lem3 4671  rankid 4682  ondomcard 4868  cardmin 4871  alephordlem1 4883  cardaleph 4896  reuunineg 6068  nnwos 6461  minvecdist 8581  fgsb 10555  fgsb2 10560

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-rab 1655

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