Theorem pm2.43i 49

Description: Inference absorbing redundant antecedent. (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 28-Nov-2008.)

Hypothesis

Ref	Expression
pm2.43i.1	|- ( ph -> ( ph -> ps ) )

Assertion

Ref	Expression
pm2.43i	|- ( ph -> ps )

Proof of Theorem pm2.43i

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ph -> ph )
2		pm2.43i.1	. 2 |- ( ph -> ( ph -> ps ) )
3	1, 2	mpd 13	1 |- ( ph -> ps )

This proof depends on syntax axioms:   -> wi 4

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

This theorem is used by:  sylc  62  impbid  129  ibi  176  anidms  401  pm2.13dc  897  hbequid  1566  equidqe  1585  equid  1753  ax10  1769  hbae  1770  vtoclgaf  2888  vtocl2gaf  2890  vtocl3gaf  2892  ifmdc  3683  elinti  3979  copsexg  4384  nlimsucg  4713  tfisi  4734  vtoclr  4823  ssrelrn  4972  issref  5170  relresfld  5317  f1o2ndf1  6464  tfrlem9  6590  nndi  6759  mulcanpig  7702  lediv2a  9227  seq3id3  10974  resqrexlemdecn  11792  ndvdssub  12713  bitsinv1  12745  nn0seqcvgd  12835  modprm0  13053  mplbasss  15136  fiinopn  15154  xmetunirn  15508  mopnval  15592  plyssc  15889  2lgsoddprm  16330  uspgrushgr  16519  uspgrupgr  16520  usgruspgr  16522  usgredg2vlem2  16562  ax1hfs  17222