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  1777  r19.36av  2685  r19.44av  2693  r19.45av  2694  reuss  3490  opthpr  3860  relop  4886  swoord2  6775  indpi  7605  lelttr  8310  elnnz  9533  ztri3or0  9565  xrlelttr  10085  icossicc  10239  iocssicc  10240  ioossico  10241  lmconst  15010  cnptopresti  15032  sslm  15041  bj-exlimmp  16470