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  2391  darii  2665  festino  2674  baroco  2676  darapti  2684  elex2OLD  3489  elex22  3490  spcimgfi1OLD  3532  vtoclegftOLD  3573  sbccomlem  3849  rspn0  4336  exel  5413  bj-axdd2  36615  bj-2exim  36634  bj-sylget  36644  bj-alexim  36650  bj-cbvalimt  36662  bj-cbveximt  36663  bj-eqs  36698  bj-nnf-exlim  36779  bj-nnflemee  36786  bj-nnflemae  36787  bj-axc10  36806  bj-alequex  36807  bj-spimtv  36817  bj-spcimdv  36918  bj-spcimdvv  36919  sn-exelALT  42236  2exim  44378  pm11.71  44396  onfrALTlem2  44546  19.41rg  44550  ax6e2nd  44558  elex2VD  44837  elex22VD  44838  onfrALTlem2VD  44888  19.41rgVD  44901  ax6e2eqVD  44906  ax6e2ndVD  44907  ax6e2ndeqVD  44908  ax6e2ndALT  44929  ax6e2ndeqALT  44930