Theorem exim 1836

Description: Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 10-Jan-1993.) (Proof shortened by Wolf Lammen, 4-Jul-2014.)

Assertion

Ref	Expression
exim	⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Proof of Theorem exim

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜓))
2	1	aleximi 1834	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1539  ∃wex 1781

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811

This theorem depends on definitions:  df-bi 206  df-ex 1782

This theorem is referenced by:  eximi  1837  19.38b  1843  19.23v  1945  alequexv  2004  nf5-1  2141  spimt  2385  darii  2660  festino  2669  baroco  2671  darapti  2679  elex2OLD  3495  elex22  3496  vtoclegftOLD  3574  spcimgft  3577  rspn0  4351  exel  5432  bj-axdd2  35458  bj-2exim  35477  bj-sylget  35486  bj-alexim  35492  bj-cbvalimt  35504  bj-cbveximt  35505  bj-eqs  35540  bj-nnf-exlim  35622  bj-nnflemee  35629  bj-nnflemae  35630  bj-axc10  35649  bj-alequex  35650  bj-spimtv  35660  bj-spcimdv  35763  bj-spcimdvv  35764  sn-exelALT  41031  2exim  43123  pm11.71  43141  onfrALTlem2  43292  19.41rg  43296  ax6e2nd  43304  elex2VD  43584  elex22VD  43585  onfrALTlem2VD  43635  19.41rgVD  43648  ax6e2eqVD  43653  ax6e2ndVD  43654  ax6e2ndeqVD  43655  ax6e2ndALT  43676  ax6e2ndeqALT  43677