Theorem pm5.16 860

Description: Theorem *5.16 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 17-Oct-2013.)

Assertion

Ref	Expression
pm5.16	|- -. ((ph <-> ps) /\ (ph <-> -. ps))

Proof of Theorem pm5.16

Step	Hyp	Ref	Expression
1		pm5.18 345	. . 3 |- ((ph <-> ps) <-> -. (ph <-> -. ps))
2	1	biimpi 186	. 2 |- ((ph <-> ps) -> -. (ph <-> -. ps))
3		imnan 411	. 2 |- (((ph <-> ps) -> -. (ph <-> -. ps)) <-> -. ((ph <-> ps) /\ (ph <-> -. ps)))
4	2, 3	mpbi 199	1 |- -. ((ph <-> ps) /\ (ph <-> -. ps))

This proof depends on syntax axioms:  -. wn 3   -> wi 4   <-> wb 176   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by: (None)