Theorem exim 1834

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 1832	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1538  ∃wex 1779

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809

This theorem depends on definitions:  df-bi 207  df-ex 1780

This theorem is referenced by:  eximi  1835  19.38b  1841  19.23v  1942  alequexv  2001  nf5-1  2146  spimt  2384  darii  2658  festino  2667  baroco  2669  darapti  2677  elex22  3472  spcimgfi1OLD  3514  vtoclegftOLD  3555  sbccomlem  3832  rspn0  4319  exel  5393  bj-axdd2  36580  bj-2exim  36599  bj-sylget  36609  bj-alexim  36615  bj-cbvalimt  36627  bj-cbveximt  36628  bj-eqs  36663  bj-nnf-exlim  36744  bj-nnflemee  36751  bj-nnflemae  36752  bj-axc10  36771  bj-alequex  36772  bj-spimtv  36782  bj-spcimdv  36883  bj-spcimdvv  36884  sn-exelALT  42206  2exim  44368  pm11.71  44386  onfrALTlem2  44536  19.41rg  44540  ax6e2nd  44548  elex2VD  44827  elex22VD  44828  onfrALTlem2VD  44878  19.41rgVD  44891  ax6e2eqVD  44896  ax6e2ndVD  44897  ax6e2ndeqVD  44898  ax6e2ndALT  44919  ax6e2ndeqALT  44920