Theorem exim 1737

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 1735	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1466  ∃wex 1692

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1698  ax-4 1711

This theorem depends on definitions:  df-bi 192  df-ex 1693

This theorem is referenced by:  eximi  1738  19.23v  1850  19.8a  1988  19.8aOLD  1989  19.9ht  2020  19.23tOLD  2045  spimt  2144  elex2  3079  elex22  3080  vtoclegft  3142  spcimgft  3146  bj-axdd2  31359  bj-2exim  31387  bj-exlimh  31393  bj-sbex  31421  bj-eqs  31456  bj-axc10  31495  bj-alequex  31496  bj-spimtv  31506  bj-spcimdv  31677  2exim  37085  pm11.71  37104  onfrALTlem2  37268  19.41rg  37273  ax6e2nd  37281  elex2VD  37582  elex22VD  37583  onfrALTlem2VD  37634  19.41rgVD  37647  ax6e2eqVD  37652  ax6e2ndVD  37653  ax6e2ndeqVD  37654  ax6e2ndALT  37675  ax6e2ndeqALT  37676