Theorem exim 1840

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 1838	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1540  ∃wex 1786

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816

This theorem depends on definitions:  df-bi 206  df-ex 1787

This theorem is referenced by:  eximi  1841  19.38b  1847  19.23v  1949  alequexv  2008  nf5-1  2145  spimt  2388  darii  2668  festino  2677  baroco  2679  darapti  2687  elex2OLD  3452  elex22  3453  vtoclegft  3521  spcimgft  3525  rspn0  4292  bj-axdd2  34770  bj-2exim  34789  bj-sylget  34798  bj-alexim  34804  bj-cbvalimt  34816  bj-cbveximt  34817  bj-eqs  34852  bj-nnf-exlim  34934  bj-nnflemee  34941  bj-nnflemae  34942  bj-axc10  34961  bj-alequex  34962  bj-spimtv  34972  bj-spcimdv  35076  bj-spcimdvv  35077  sn-el  40184  2exim  41967  pm11.71  41985  onfrALTlem2  42136  19.41rg  42140  ax6e2nd  42148  elex2VD  42428  elex22VD  42429  onfrALTlem2VD  42479  19.41rgVD  42492  ax6e2eqVD  42497  ax6e2ndVD  42498  ax6e2ndeqVD  42499  ax6e2ndALT  42520  ax6e2ndeqALT  42521