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  726  pm2.621  747  orim1d  787  orim2d  788  pm2.63  800  pm2.74  807  simprimdc  859  oplem1  975  equsex  1728  equsexd  1729  r19.36av  2628  r19.44av  2636  r19.45av  2637  reuss  3416  opthpr  3772  relop  4777  swoord2  6564  indpi  7340  lelttr  8044  elnnz  9261  ztri3or0  9293  xrlelttr  9804  icossicc  9958  iocssicc  9959  ioossico  9960  lmconst  13609  cnptopresti  13631  sslm  13640  bj-exlimmp  14403