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  731  pm2.621  752  orim1d  792  orim2d  793  pm2.63  805  pm2.74  812  simprimdc  864  oplem1  981  equsex  1774  equsexd  1775  r19.36av  2682  r19.44av  2690  r19.45av  2691  reuss  3485  opthpr  3849  relop  4871  swoord2  6708  indpi  7525  lelttr  8231  elnnz  9452  ztri3or0  9484  xrlelttr  9998  icossicc  10152  iocssicc  10153  ioossico  10154  lmconst  14884  cnptopresti  14906  sslm  14915  bj-exlimmp  16091