Theorem exim 1909

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 1907	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1629  ∃wex 1852

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885

This theorem depends on definitions:  df-bi 197  df-ex 1853

This theorem is referenced by:  eximi  1910  19.38b  1917  19.38bOLD  1918  19.23v  2023  19.23vOLD  2071  nf5-1  2178  19.8a  2206  19.9ht  2308  spimt  2415  elex2  3368  elex22  3369  vtoclegft  3432  spcimgft  3436  bj-axdd2  32914  bj-2exim  32933  bj-exlimh  32940  bj-alexim  32943  bj-sbex  32965  bj-alequexv  32993  bj-eqs  33001  bj-axc10  33045  bj-alequex  33046  bj-spimtv  33056  bj-spcimdv  33214  bj-spcimdvv  33215  2exim  39105  pm11.71  39124  onfrALTlem2  39287  19.41rg  39292  ax6e2nd  39300  elex2VD  39596  elex22VD  39597  onfrALTlem2VD  39648  19.41rgVD  39661  ax6e2eqVD  39666  ax6e2ndVD  39667  ax6e2ndeqVD  39668  ax6e2ndALT  39689  ax6e2ndeqALT  39690