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Theorem nfmpt1 3878
Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by FL, 17-Feb-2008.)
Assertion
Ref Expression
nfmpt1 𝑥(𝑥𝐴𝐵)

Proof of Theorem nfmpt1
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 df-mpt 3848 . 2 (𝑥𝐴𝐵) = {⟨𝑥, 𝑧⟩ ∣ (𝑥𝐴𝑧 = 𝐵)}
2 nfopab1 3854 . 2 𝑥{⟨𝑥, 𝑧⟩ ∣ (𝑥𝐴𝑧 = 𝐵)}
31, 2nfcxfr 2191 1 𝑥(𝑥𝐴𝐵)
Colors of variables: wff set class
Syntax hints:  wa 101   = wceq 1259  wcel 1409  wnfc 2181  {copab 3845  cmpt 3846
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-opab 3847  df-mpt 3848
This theorem is referenced by:  nffvmpt1  5214  fvmptss2  5275  fvmptssdm  5283  fvmptdf  5286  mpteqb  5289  fvmptf  5291  ralrnmpt  5337  rexrnmpt  5338  f1ompt  5348  f1mpt  5438  fliftfun  5464  dom2lem  6283
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