MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  sb3an Unicode version

Theorem sb3an 2141
Description: Conjunction inside and outside of a substitution are equivalent. (Contributed by NM, 14-Dec-2006.)
Assertion
Ref Expression
sb3an

Proof of Theorem sb3an
StepHypRef Expression
1 df-3an 975 . . 3
21sbbii 1746 . 2
3 sban 2140 . 2
4 sban 2140 . . . 4
54anbi1i 695 . . 3
6 df-3an 975 . . 3
75, 6bitr4i 252 . 2
82, 3, 73bitri 271 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  /\w3a 973  [wsb 1739
This theorem is referenced by:  sbc3angOLD  3391
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-ex 1613  df-nf 1617  df-sb 1740
  Copyright terms: Public domain W3C validator