Theorem imnan 411

Description: Express implication in terms of conjunction. (Contributed by NM, 9-Apr-1994.)

Assertion

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

Proof of Theorem imnan

Step	Hyp	Ref	Expression
1		df-an 360	. 2 |- ((ph /\ ps) <-> -. (ph -> -. ps))
2	1	con2bii 322	1 |- ((ph -> -. ps) <-> -. (ph /\ ps))

Syntax hints:  -. wn 3   -> wi 4   <-> wb 176   /\ wa 358

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8

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

This theorem is referenced by:  imnani  412  iman  413  ianor  474  nan  563  pm5.17  858  pm5.16  860  dn1  932  nic-ax  1438  nic-axALT  1439  alinexa  1578  dfsb3  2056  ralinexa  2659  pssn2lp  3370  minel  3606  disjsn  3786  ltfinirr  4457  tfinltfin  4501  evenodddisj  4516  funun  5146  imadif  5171  nmembers1lem2  6269  nmembers1lem3  6270