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Theorem nfmpt1 5672
 Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by FL, 17-Feb-2008.)
Assertion
Ref Expression
nfmpt1 x(x A B)

Proof of Theorem nfmpt1
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 df-mpt 5652 . 2 (x A B) = {x, z (x A z = B)}
2 nfopab1 4628 . 2 x{x, z (x A z = B)}
31, 2nfcxfr 2486 1 x(x A B)
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 358   = wceq 1642   ∈ wcel 1710  Ⅎwnfc 2476  {copab 4622   ↦ cmpt 5651 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  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 2478  df-opab 4623  df-mpt 5652 This theorem is referenced by:  fvmptss  5705  fvmptf  5722
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