Theorem exim 1857

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 23	. 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜓))
2	1	aleximi 1855	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1561  ∃wex 1802

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832

This theorem depends on definitions:  df-bi 210  df-ex 1803

This theorem is referenced by:  eximi  1858  19.38b  1864  19.23v  1965  alequexv  2024  nf5-1  2182  spimt  2420  darii  2694  festino  2703  baroco  2705  darapti  2713  elex22  3481  spcimgfi1OLD  3519  sbccomlem  3825  rspn0  4312  replem  5243  exel  5406  bj-axdd2  37047  bj-2exim  37085  bj-sylget  37088  bj-alexim  37095  bj-aleximiALT  37096  bj-eqs  37160  bj-nnf-exlim  37247  bj-nnflemee  37274  bj-nnflemae  37275  bj-axc10  37280  bj-alequex  37281  bj-spimtv  37291  bj-spcimdv  37392  bj-spcimdvv  37393  bj-axreprepsep  37572  sn-exelALT  42850  2exim  44953  pm11.71  44971  onfrALTlem2  45120  19.41rg  45124  ax6e2nd  45132  elex2VD  45411  elex22VD  45412  onfrALTlem2VD  45462  19.41rgVD  45475  ax6e2eqVD  45480  ax6e2ndVD  45481  ax6e2ndeqVD  45482  ax6e2ndALT  45503  ax6e2ndeqALT  45504