Theorem exim 1832

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 1830	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1535  ∃wex 1777

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807

This theorem depends on definitions:  df-bi 207  df-ex 1778

This theorem is referenced by:  eximi  1833  19.38b  1839  19.23v  1941  alequexv  2000  nf5-1  2145  spimt  2394  darii  2668  festino  2677  baroco  2679  darapti  2687  elex2OLD  3513  elex22  3514  spcimgfi1OLD  3560  vtoclegftOLD  3602  sbccomlem  3891  rspn0  4379  exel  5453  bj-axdd2  36558  bj-2exim  36577  bj-sylget  36587  bj-alexim  36593  bj-cbvalimt  36605  bj-cbveximt  36606  bj-eqs  36641  bj-nnf-exlim  36722  bj-nnflemee  36729  bj-nnflemae  36730  bj-axc10  36749  bj-alequex  36750  bj-spimtv  36760  bj-spcimdv  36861  bj-spcimdvv  36862  sn-exelALT  42211  2exim  44348  pm11.71  44366  onfrALTlem2  44517  19.41rg  44521  ax6e2nd  44529  elex2VD  44809  elex22VD  44810  onfrALTlem2VD  44860  19.41rgVD  44873  ax6e2eqVD  44878  ax6e2ndVD  44879  ax6e2ndeqVD  44880  ax6e2ndALT  44901  ax6e2ndeqALT  44902