Theorem exim 1833

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 1831	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1537  ∃wex 1778

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808

This theorem depends on definitions:  df-bi 207  df-ex 1779

This theorem is referenced by:  eximi  1834  19.38b  1840  19.23v  1941  alequexv  1999  nf5-1  2144  spimt  2390  darii  2664  festino  2673  baroco  2675  darapti  2683  elex2OLD  3504  elex22  3505  spcimgfi1OLD  3547  vtoclegftOLD  3588  sbccomlem  3868  rspn0  4355  exel  5437  bj-axdd2  36594  bj-2exim  36613  bj-sylget  36623  bj-alexim  36629  bj-cbvalimt  36641  bj-cbveximt  36642  bj-eqs  36677  bj-nnf-exlim  36758  bj-nnflemee  36765  bj-nnflemae  36766  bj-axc10  36785  bj-alequex  36786  bj-spimtv  36796  bj-spcimdv  36897  bj-spcimdvv  36898  sn-exelALT  42258  2exim  44403  pm11.71  44421  onfrALTlem2  44571  19.41rg  44575  ax6e2nd  44583  elex2VD  44863  elex22VD  44864  onfrALTlem2VD  44914  19.41rgVD  44927  ax6e2eqVD  44932  ax6e2ndVD  44933  ax6e2ndeqVD  44934  ax6e2ndALT  44955  ax6e2ndeqALT  44956