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Theorem nfmpt2 5675
 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 5654 . 2
2 nfmpt2.1 . . . . . 6
32nfcri 2483 . . . . 5
4 nfmpt2.2 . . . . . 6
54nfcri 2483 . . . . 5
63, 5nfan 1824 . . . 4
7 nfmpt2.3 . . . . 5
87nfeq2 2500 . . . 4
96, 8nfan 1824 . . 3
109nfoprab 5549 . 2
111, 10nfcxfr 2486 1
 Colors of variables: wff setvar class Syntax hints:   wa 358   wceq 1642   wcel 1710  wnfc 2476  coprab 5527   cmpt2 5653 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-oprab 5528  df-mpt2 5654 This theorem is referenced by: (None)
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