Theorem idd 21

Description: Principle of identity with antecedent. (Contributed by NM, 26-Nov-1995.)

Assertion

Ref	Expression
idd	|- ( ph -> ( ps -> ps ) )

Proof of Theorem idd

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ps -> ps )
2	1	a1i 9	1 |- ( ph -> ( ps -> ps ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  imim1d  75  ancld  325  ancrd  326  anim12d  335  anim1d  336  anim2d  337  orel2  727  pm2.621  748  orim1d  788  orim2d  789  pm2.63  801  pm2.74  808  simprimdc  860  oplem1  977  equsex  1750  equsexd  1751  r19.36av  2656  r19.44av  2664  r19.45av  2665  reuss  3453  opthpr  3812  relop  4827  swoord2  6649  indpi  7454  lelttr  8160  elnnz  9381  ztri3or0  9413  xrlelttr  9927  icossicc  10081  iocssicc  10082  ioossico  10083  lmconst  14659  cnptopresti  14681  sslm  14690  bj-exlimmp  15667