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  738  pm2.621  759  orim1d  799  orim2d  800  pm2.63  812  pm2.74  819  simprimdc  871  oplem1  988  equsex  1780  equsexd  1782  r19.36av  2702  r19.44av  2710  r19.45av  2711  reuss  3514  opthpr  3895  relop  4928  swoord2  6831  indpi  7703  lelttr  8408  elnnz  9637  ztri3or0  9669  xrlelttr  10191  icossicc  10345  iocssicc  10346  ioossico  10347  issubassa3  14995  lmconst  15300  cnptopresti  15322  sslm  15331  bj-exlimmp  16780