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Theorem nfmpt2 6134
 Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by NM, 20-Feb-2013.)
Hypotheses
Ref Expression
nfmpt2.1
nfmpt2.2
nfmpt2.3
Assertion
Ref Expression
nfmpt2
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)   (,,)   (,,)

Proof of Theorem nfmpt2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-mpt2 6078 . 2
2 nfmpt2.1 . . . . . 6
32nfcri 2565 . . . . 5
4 nfmpt2.2 . . . . . 6
54nfcri 2565 . . . . 5
63, 5nfan 1846 . . . 4
7 nfmpt2.3 . . . . 5
87nfeq2 2582 . . . 4
96, 8nfan 1846 . . 3
109nfoprab 6118 . 2
111, 10nfcxfr 2568 1
 Colors of variables: wff set class Syntax hints:   wa 359   wceq 1652   wcel 1725  wnfc 2558  coprab 6074   cmpt2 6075 This theorem is referenced by:  nfseq  11325  ptbasfi  17605  sdclem1  26438  fmuldfeqlem1  27679  stoweidlem51  27767 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-oprab 6077  df-mpt2 6078
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