HomeHome Metamath Proof Explorer < Previous   Next >
Related theorems
Unicode version
Theorem pm5.16 665
Description: Theorem *5.16 of [WhiteheadRussell] p. 124.
Assertion
Ref Expression
pm5.16 |- -. ((ph <-> ps) /\ (ph <-> -. ps))
Proof of Theorem pm5.16
StepHypRef Expression
1 pm5.18 658 . . . 4 |- ((ph <-> ps) <-> -. (ph <-> -. ps))
21biimp 151 . . 3 |- ((ph <-> ps) -> -. (ph <-> -. ps))
3 pm4.62 235 . . 3 |- (((ph <-> ps) -> -. (ph <-> -. ps)) <-> (-. (ph <-> ps) \/ -. (ph <-> -. ps)))
42, 3mpbi 189 . 2 |- (-. (ph <-> ps) \/ -. (ph <-> -. ps))
5 ianor 305 . 2 |- (-. ((ph <-> ps) /\ (ph <-> -. ps)) <-> (-. (ph <-> ps) \/ -. (ph <-> -. ps)))
64, 5mpbir 190 1 |- -. ((ph <-> ps) /\ (ph <-> -. ps))
Colors of variables: wff set class
Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   \/ wo 222   /\ wa 223
This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7
This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225
Copyright terms: Public domain