Theorem exim 1831

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 1829	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1535  ∃wex 1776

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806

This theorem depends on definitions:  df-bi 207  df-ex 1777

This theorem is referenced by:  eximi  1832  19.38b  1838  19.23v  1940  alequexv  1998  nf5-1  2143  spimt  2389  darii  2663  festino  2672  baroco  2674  darapti  2682  elex2OLD  3503  elex22  3504  spcimgfi1OLD  3548  vtoclegftOLD  3589  sbccomlem  3878  rspn0  4362  exel  5444  bj-axdd2  36575  bj-2exim  36594  bj-sylget  36604  bj-alexim  36610  bj-cbvalimt  36622  bj-cbveximt  36623  bj-eqs  36658  bj-nnf-exlim  36739  bj-nnflemee  36746  bj-nnflemae  36747  bj-axc10  36766  bj-alequex  36767  bj-spimtv  36777  bj-spcimdv  36878  bj-spcimdvv  36879  sn-exelALT  42236  2exim  44375  pm11.71  44393  onfrALTlem2  44544  19.41rg  44548  ax6e2nd  44556  elex2VD  44836  elex22VD  44837  onfrALTlem2VD  44887  19.41rgVD  44900  ax6e2eqVD  44905  ax6e2ndVD  44906  ax6e2ndeqVD  44907  ax6e2ndALT  44928  ax6e2ndeqALT  44929