Theorem exim 1751

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 1749	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1473  ∃wex 1695

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728

This theorem depends on definitions:  df-bi 196  df-ex 1696

This theorem is referenced by:  eximi  1752  19.23v  1889  nf5-1  2010  19.8a  2039  19.8aOLD  2040  19.9ht  2128  spimt  2241  elex2  3189  elex22  3190  vtoclegft  3253  spcimgft  3257  bj-axdd2  31749  bj-2exim  31780  bj-exlimh  31787  bj-sbex  31815  bj-eqs  31850  bj-axc10  31894  bj-alequex  31895  bj-spimtv  31905  bj-spcimdv  32078  wl-nf-nf2  32463  2exim  37600  pm11.71  37619  onfrALTlem2  37782  19.41rg  37787  ax6e2nd  37795  elex2VD  38095  elex22VD  38096  onfrALTlem2VD  38147  19.41rgVD  38160  ax6e2eqVD  38165  ax6e2ndVD  38166  ax6e2ndeqVD  38167  ax6e2ndALT  38188  ax6e2ndeqALT  38189