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  2696  r19.44av  2704  r19.45av  2705  reuss  3506  opthpr  3881  relop  4910  swoord2  6810  indpi  7673  lelttr  8378  elnnz  9604  ztri3or0  9636  xrlelttr  10158  icossicc  10312  iocssicc  10313  ioossico  10314  lmconst  15207  cnptopresti  15229  sslm  15238  bj-exlimmp  16667