Theorem exim 1898

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 1896	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1618  ∃wex 1841

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1859  ax-4 1874

This theorem depends on definitions:  df-bi 197  df-ex 1842

This theorem is referenced by:  eximi  1899  19.38b  1905  19.23v  2008  19.23vOLD  2056  nf5-1  2160  19.8a  2187  19.9ht  2278  spimt  2386  elex2  3344  elex22  3345  vtoclegft  3408  spcimgft  3412  bj-axdd2  32853  bj-2exim  32872  bj-exlimh  32879  bj-alexim  32882  bj-sbex  32903  bj-alequexv  32932  bj-eqs  32940  bj-axc10  32984  bj-alequex  32985  bj-spimtv  32995  bj-spcimdv  33161  bj-spcimdvv  33162  2exim  39049  pm11.71  39068  onfrALTlem2  39232  19.41rg  39237  ax6e2nd  39245  elex2VD  39541  elex22VD  39542  onfrALTlem2VD  39593  19.41rgVD  39606  ax6e2eqVD  39611  ax6e2ndVD  39612  ax6e2ndeqVD  39613  ax6e2ndALT  39634  ax6e2ndeqALT  39635