Theorem exim 1835

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 1833	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1539  ∃wex 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810

This theorem depends on definitions:  df-bi 207  df-ex 1781

This theorem is referenced by:  eximi  1836  19.38b  1842  19.23v  1943  alequexv  2002  nf5-1  2150  spimt  2390  darii  2665  festino  2674  baroco  2676  darapti  2684  elex22  3465  spcimgfi1OLD  3505  sbccomlem  3819  rspn0  4308  exel  5383  bj-axdd2  36792  bj-2exim  36811  bj-sylget  36821  bj-alexim  36827  bj-cbvalimt  36839  bj-cbveximt  36840  bj-eqs  36876  bj-nnf-exlim  36957  bj-nnflemee  36964  bj-nnflemae  36965  bj-axc10  36984  bj-alequex  36985  bj-spimtv  36995  bj-spcimdv  37096  bj-spcimdvv  37097  sn-exelALT  42471  2exim  44616  pm11.71  44634  onfrALTlem2  44783  19.41rg  44787  ax6e2nd  44795  elex2VD  45074  elex22VD  45075  onfrALTlem2VD  45125  19.41rgVD  45138  ax6e2eqVD  45143  ax6e2ndVD  45144  ax6e2ndeqVD  45145  ax6e2ndALT  45166  ax6e2ndeqALT  45167