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  727  pm2.621  748  orim1d  788  orim2d  789  pm2.63  801  pm2.74  808  simprimdc  860  oplem1  977  equsex  1742  equsexd  1743  r19.36av  2648  r19.44av  2656  r19.45av  2657  reuss  3445  opthpr  3803  relop  4817  swoord2  6631  indpi  7428  lelttr  8134  elnnz  9355  ztri3or0  9387  xrlelttr  9900  icossicc  10054  iocssicc  10055  ioossico  10056  lmconst  14560  cnptopresti  14582  sslm  14591  bj-exlimmp  15523