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  3467  spcimgfi1OLD  3507  sbccomlem  3821  rspn0  4310  exel  5390  bj-axdd2  36813  bj-2exim  36843  bj-sylget  36848  bj-alexim  36855  bj-aleximiALT  36856  bj-cbvalimt  36869  bj-cbveximt  36870  bj-eqs  36914  bj-nnf-exlim  36997  bj-nnflemee  37019  bj-nnflemae  37020  bj-axc10  37025  bj-alequex  37026  bj-spimtv  37036  bj-spcimdv  37137  bj-spcimdvv  37138  bj-axreprepsep  37317  sn-exelALT  42585  2exim  44729  pm11.71  44747  onfrALTlem2  44896  19.41rg  44900  ax6e2nd  44908  elex2VD  45187  elex22VD  45188  onfrALTlem2VD  45238  19.41rgVD  45251  ax6e2eqVD  45256  ax6e2ndVD  45257  ax6e2ndeqVD  45258  ax6e2ndALT  45279  ax6e2ndeqALT  45280