Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm11.07 Unicode version

Theorem pm11.07 2078
 Description: Theorem *11.07 in [WhiteheadRussell] p. 159. (Contributed by Andrew Salmon, 17-Jun-2011.)
Assertion
Ref Expression
pm11.07
Distinct variable groups:   ,,,   ,,
Allowed substitution hint:   ()

Proof of Theorem pm11.07
StepHypRef Expression
1 a9e 1817 . . . . . . 7
2 a9e 1817 . . . . . . 7
31, 2pm3.2i 443 . . . . . 6
4 a9e 1817 . . . . . . 7
5 a9e 1817 . . . . . . 7
64, 5pm3.2i 443 . . . . . 6
73, 62th 232 . . . . 5
8 eeanv 2058 . . . . 5
9 eeanv 2058 . . . . 5
107, 8, 93bitr4i 270 . . . 4
1110anbi1i 679 . . 3
12 19.41vv 2036 . . 3
13 19.41vv 2036 . . 3
1411, 12, 133bitr4i 270 . 2
15 2sb5 2075 . 2
16 2sb5 2075 . 2
1714, 15, 163bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  wex 1537   wceq 1619  wsb 1883 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884
 Copyright terms: Public domain W3C validator