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  1739  equsexd  1740  r19.36av  2645  r19.44av  2653  r19.45av  2654  reuss  3440  opthpr  3798  relop  4812  swoord2  6617  indpi  7402  lelttr  8108  elnnz  9327  ztri3or0  9359  xrlelttr  9872  icossicc  10026  iocssicc  10027  ioossico  10028  lmconst  14384  cnptopresti  14406  sslm  14415  bj-exlimmp  15261