Mathbox for Wolf Lammen < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  wl-sbcom2d-lem1 Structured version   Visualization version   Unicode version

Theorem wl-sbcom2d-lem1 31959
 Description: Lemma used to prove wl-sbcom2d 31961. (Contributed by Wolf Lammen, 10-Aug-2019.) (New usage is discouraged.)
Assertion
Ref Expression
wl-sbcom2d-lem1
Distinct variable groups:   ,,   ,,   ,,   ,,   ,,
Allowed substitution hints:   (,,,)

Proof of Theorem wl-sbcom2d-lem1
StepHypRef Expression
1 nfna1 2005 . . . . . 6
2 nfeqf2 2148 . . . . . 6
31, 2nfan1 2030 . . . . 5
4 sbequ 2225 . . . . . 6
54adantl 473 . . . . 5
63, 5sbbid 2252 . . . 4
76ancoms 460 . . 3
8 sbequ 2225 . . 3
97, 8sylan9bbr 715 . 2
109expr 626 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 189   wa 376  wal 1450  wsb 1805 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950  ax-13 2104 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-ex 1672  df-nf 1676  df-sb 1806 This theorem is referenced by:  wl-sbcom2d  31961
 Copyright terms: Public domain W3C validator