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Theorem bj-df-ifc 31159
 Description: The definition of "ifc" if "if-" enters the main part. This is in line with the definition of a class as the extension of a predicate in df-clab 2438. (Contributed by BJ, 20-Sep-2019.)
Assertion
Ref Expression
bj-df-ifc if-
Distinct variable groups:   ,   ,   ,

Proof of Theorem bj-df-ifc
StepHypRef Expression
1 bj-dfifc2 31158 . 2
2 df-ifp 1426 . . . 4 if-
32bicomi 206 . . 3 if-
43abbii 2567 . 2 if-
51, 4eqtri 2473 1 if-
 Colors of variables: wff setvar class Syntax hints:   wn 3   wo 370   wa 371  if-wif 1425   wceq 1444   wcel 1887  cab 2437  cif 3881 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-ifp 1426  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-if 3882 This theorem is referenced by:  bj-ififc  31160
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