Theorem exim 1836

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 1834	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1540  ∃wex 1781

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811

This theorem depends on definitions:  df-bi 207  df-ex 1782

This theorem is referenced by:  eximi  1837  19.38b  1843  19.23v  1944  alequexv  2003  nf5-1  2151  spimt  2390  darii  2665  festino  2674  baroco  2676  darapti  2684  elex22  3454  spcimgfi1OLD  3493  sbccomlem  3807  rspn0  4296  replem  5223  exel  5386  bj-axdd2  36857  bj-2exim  36895  bj-sylget  36898  bj-alexim  36905  bj-aleximiALT  36906  bj-eqs  36970  bj-nnf-exlim  37057  bj-nnflemee  37084  bj-nnflemae  37085  bj-axc10  37090  bj-alequex  37091  bj-spimtv  37101  bj-spcimdv  37202  bj-spcimdvv  37203  bj-axreprepsep  37382  sn-exelALT  42660  2exim  44806  pm11.71  44824  onfrALTlem2  44973  19.41rg  44977  ax6e2nd  44985  elex2VD  45264  elex22VD  45265  onfrALTlem2VD  45315  19.41rgVD  45328  ax6e2eqVD  45333  ax6e2ndVD  45334  ax6e2ndeqVD  45335  ax6e2ndALT  45356  ax6e2ndeqALT  45357