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  734  pm2.621  755  orim1d  795  orim2d  796  pm2.63  808  pm2.74  815  simprimdc  867  oplem1  984  equsex  1776  equsexd  1778  r19.36av  2694  r19.44av  2702  r19.45av  2703  reuss  3502  opthpr  3876  relop  4905  swoord2  6797  indpi  7657  lelttr  8362  elnnz  9587  ztri3or0  9619  xrlelttr  10139  icossicc  10293  iocssicc  10294  ioossico  10295  lmconst  15081  cnptopresti  15103  sslm  15112  bj-exlimmp  16541