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Theorem nfmpo 5806
 Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by NM, 20-Feb-2013.)
Hypotheses
Ref Expression
nfmpo.1
nfmpo.2
nfmpo.3
Assertion
Ref Expression
nfmpo
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)   (,,)   (,,)

Proof of Theorem nfmpo
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-mpo 5745 . 2
2 nfmpo.1 . . . . . 6
32nfcri 2250 . . . . 5
4 nfmpo.2 . . . . . 6
54nfcri 2250 . . . . 5
63, 5nfan 1527 . . . 4
7 nfmpo.3 . . . . 5
87nfeq2 2268 . . . 4
96, 8nfan 1527 . . 3
109nfoprab 5789 . 2
111, 10nfcxfr 2253 1
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1314   wcel 1463  wnfc 2243  coprab 5741   cmpo 5742 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-oprab 5744  df-mpo 5745 This theorem is referenced by:  nfof  5953  nfseq  10179
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