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Theorem hbab1 2342
 Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
hbab1 (y {x φ} → x y {x φ})
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y)

Proof of Theorem hbab1
StepHypRef Expression
1 df-clab 2340 . 2 (y {x φ} ↔ [y / x]φ)
2 hbs1 2105 . 2 ([y / x]φx[y / x]φ)
31, 2hbxfrbi 1568 1 (y {x φ} → x y {x φ})
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540  [wsb 1648   ∈ wcel 1710  {cab 2339 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 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 This theorem is referenced by:  nfsab1  2343  abeq2  2458
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