Theorem idd 21

Description: Principle of identity with antecedent. (Contributed by NM, 26-Nov-1995.)

Assertion

Ref	Expression
idd	⊢ (𝜑 → (𝜓 → 𝜓))

Proof of Theorem idd

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (𝜓 → 𝜓)
2	1	a1i 9	1 ⊢ (𝜑 → (𝜓 → 𝜓))

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  3504  opthpr  3878  relop  4907  swoord2  6799  indpi  7662  lelttr  8367  elnnz  9592  ztri3or0  9624  xrlelttr  10145  icossicc  10299  iocssicc  10300  ioossico  10301  lmconst  15130  cnptopresti  15152  sslm  15161  bj-exlimmp  16590