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  733  pm2.621  754  orim1d  794  orim2d  795  pm2.63  807  pm2.74  814  simprimdc  866  oplem1  983  equsex  1776  equsexd  1777  r19.36av  2684  r19.44av  2692  r19.45av  2693  reuss  3488  opthpr  3855  relop  4880  swoord2  6732  indpi  7562  lelttr  8268  elnnz  9489  ztri3or0  9521  xrlelttr  10041  icossicc  10195  iocssicc  10196  ioossico  10197  lmconst  14943  cnptopresti  14965  sslm  14974  bj-exlimmp  16386