Theorem pm4.61 442

Description: Theorem *4.61 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.61	|- ( -. ( ph -> ps ) <-> ( ph /\ -. ps ) )

Proof of Theorem pm4.61

Step	Hyp	Ref	Expression
1		annim 441	. 2 |- ( ( ph /\ -. ps ) <-> -. ( ph -> ps ) )
2	1	bicomi 214	1 |- ( -. ( ph -> ps ) <-> ( ph /\ -. ps ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   /\ wa 384

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

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  pm4.65  443  npss  3717  difin  3861  isf32lem2  9176  nmo  29325  bnj1253  31085  unblimceq0  32498  fphpd  37380  rp-fakenanass  37860  clsk1independent  38344  nabctnabc  41098  islindeps  42242