Theorem exim 1837

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 1835	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1540  ∃wex 1782

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812

This theorem depends on definitions:  df-bi 206  df-ex 1783

This theorem is referenced by:  eximi  1838  19.38b  1844  19.23v  1946  alequexv  2005  nf5-1  2142  spimt  2386  darii  2661  festino  2670  baroco  2672  darapti  2680  elex2OLD  3496  elex22  3497  vtoclegftOLD  3575  spcimgft  3578  rspn0  4353  exel  5434  bj-axdd2  35470  bj-2exim  35489  bj-sylget  35498  bj-alexim  35504  bj-cbvalimt  35516  bj-cbveximt  35517  bj-eqs  35552  bj-nnf-exlim  35634  bj-nnflemee  35641  bj-nnflemae  35642  bj-axc10  35661  bj-alequex  35662  bj-spimtv  35672  bj-spcimdv  35775  bj-spcimdvv  35776  sn-exelALT  41035  2exim  43138  pm11.71  43156  onfrALTlem2  43307  19.41rg  43311  ax6e2nd  43319  elex2VD  43599  elex22VD  43600  onfrALTlem2VD  43650  19.41rgVD  43663  ax6e2eqVD  43668  ax6e2ndVD  43669  ax6e2ndeqVD  43670  ax6e2ndALT  43691  ax6e2ndeqALT  43692