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Theorem nfmpt 5671
 Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by NM, 20-Feb-2013.)
Hypotheses
Ref Expression
nfmpt.1 xA
nfmpt.2 xB
Assertion
Ref Expression
nfmpt x(y A B)
Distinct variable group:   x,y
Allowed substitution hints:   A(x,y)   B(x,y)

Proof of Theorem nfmpt
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 df-mpt 5652 . 2 (y A B) = {y, z (y A z = B)}
2 nfmpt.1 . . . . 5 xA
32nfcri 2483 . . . 4 x y A
4 nfmpt.2 . . . . 5 xB
54nfeq2 2500 . . . 4 x z = B
63, 5nfan 1824 . . 3 x(y A z = B)
76nfopab 4627 . 2 x{y, z (y A z = B)}
81, 7nfcxfr 2486 1 x(y 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-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-or 359  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: (None)
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