Theorem exim 1835

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 1833	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1539  ∃wex 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810

This theorem depends on definitions:  df-bi 207  df-ex 1781

This theorem is referenced by:  eximi  1836  19.38b  1842  19.23v  1943  alequexv  2002  nf5-1  2150  spimt  2388  darii  2662  festino  2671  baroco  2673  darapti  2681  elex22  3462  spcimgfi1OLD  3502  sbccomlem  3816  rspn0  4305  exel  5378  bj-axdd2  36657  bj-2exim  36676  bj-sylget  36686  bj-alexim  36692  bj-cbvalimt  36704  bj-cbveximt  36705  bj-eqs  36740  bj-nnf-exlim  36821  bj-nnflemee  36828  bj-nnflemae  36829  bj-axc10  36848  bj-alequex  36849  bj-spimtv  36859  bj-spcimdv  36960  bj-spcimdvv  36961  sn-exelALT  42337  2exim  44497  pm11.71  44515  onfrALTlem2  44664  19.41rg  44668  ax6e2nd  44676  elex2VD  44955  elex22VD  44956  onfrALTlem2VD  45006  19.41rgVD  45019  ax6e2eqVD  45024  ax6e2ndVD  45025  ax6e2ndeqVD  45026  ax6e2ndALT  45047  ax6e2ndeqALT  45048