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  731  pm2.621  752  orim1d  792  orim2d  793  pm2.63  805  pm2.74  812  simprimdc  864  oplem1  981  equsex  1774  equsexd  1775  r19.36av  2682  r19.44av  2690  r19.45av  2691  reuss  3486  opthpr  3853  relop  4878  swoord2  6727  indpi  7555  lelttr  8261  elnnz  9482  ztri3or0  9514  xrlelttr  10034  icossicc  10188  iocssicc  10189  ioossico  10190  lmconst  14933  cnptopresti  14955  sslm  14964  bj-exlimmp  16315