Theorem exim 1835

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 1833	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1539  ∃wex 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810

This theorem depends on definitions:  df-bi 207  df-ex 1781

This theorem is referenced by:  eximi  1836  19.38b  1842  19.23v  1943  alequexv  2002  nf5-1  2148  spimt  2386  darii  2660  festino  2669  baroco  2671  darapti  2679  elex22  3461  spcimgfi1OLD  3503  vtoclegftOLD  3544  sbccomlem  3820  rspn0  4306  exel  5376  bj-axdd2  36632  bj-2exim  36651  bj-sylget  36661  bj-alexim  36667  bj-cbvalimt  36679  bj-cbveximt  36680  bj-eqs  36715  bj-nnf-exlim  36796  bj-nnflemee  36803  bj-nnflemae  36804  bj-axc10  36823  bj-alequex  36824  bj-spimtv  36834  bj-spcimdv  36935  bj-spcimdvv  36936  sn-exelALT  42257  2exim  44418  pm11.71  44436  onfrALTlem2  44585  19.41rg  44589  ax6e2nd  44597  elex2VD  44876  elex22VD  44877  onfrALTlem2VD  44927  19.41rgVD  44940  ax6e2eqVD  44945  ax6e2ndVD  44946  ax6e2ndeqVD  44947  ax6e2ndALT  44968  ax6e2ndeqALT  44969