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  2391  darii  2666  festino  2675  baroco  2677  darapti  2685  elex22  3455  spcimgfi1OLD  3494  sbccomlem  3808  rspn0  4297  replem  5223  exel  5381  bj-axdd2  36873  bj-2exim  36911  bj-sylget  36914  bj-alexim  36921  bj-aleximiALT  36922  bj-eqs  36986  bj-nnf-exlim  37073  bj-nnflemee  37100  bj-nnflemae  37101  bj-axc10  37106  bj-alequex  37107  bj-spimtv  37117  bj-spcimdv  37218  bj-spcimdvv  37219  bj-axreprepsep  37398  sn-exelALT  42674  2exim  44824  pm11.71  44842  onfrALTlem2  44991  19.41rg  44995  ax6e2nd  45003  elex2VD  45282  elex22VD  45283  onfrALTlem2VD  45333  19.41rgVD  45346  ax6e2eqVD  45351  ax6e2ndVD  45352  ax6e2ndeqVD  45353  ax6e2ndALT  45374  ax6e2ndeqALT  45375