Theorem exim 1833

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 1831	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1537  ∃wex 1778

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808

This theorem depends on definitions:  df-bi 207  df-ex 1779

This theorem is referenced by:  eximi  1834  19.38b  1840  19.23v  1941  alequexv  1999  nf5-1  2144  spimt  2389  darii  2663  festino  2672  baroco  2674  darapti  2682  elex2OLD  3488  elex22  3489  spcimgfi1OLD  3531  vtoclegftOLD  3572  sbccomlem  3849  rspn0  4336  exel  5418  bj-axdd2  36568  bj-2exim  36587  bj-sylget  36597  bj-alexim  36603  bj-cbvalimt  36615  bj-cbveximt  36616  bj-eqs  36651  bj-nnf-exlim  36732  bj-nnflemee  36739  bj-nnflemae  36740  bj-axc10  36759  bj-alequex  36760  bj-spimtv  36770  bj-spcimdv  36871  bj-spcimdvv  36872  sn-exelALT  42232  2exim  44370  pm11.71  44388  onfrALTlem2  44538  19.41rg  44542  ax6e2nd  44550  elex2VD  44830  elex22VD  44831  onfrALTlem2VD  44881  19.41rgVD  44894  ax6e2eqVD  44899  ax6e2ndVD  44900  ax6e2ndeqVD  44901  ax6e2ndALT  44922  ax6e2ndeqALT  44923