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 1536  ∃wex 1781

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811

This theorem depends on definitions:  df-bi 210  df-ex 1782

This theorem is referenced by:  eximi  1836  19.38b  1842  19.23v  1943  alequexv  2007  nf5-1  2146  spimt  2393  darii  2727  festino  2736  baroco  2738  darapti  2746  elex2  3463  elex22  3464  vtoclegft  3530  spcimgft  3534  rspn0  4266  bj-axdd2  34039  bj-2exim  34058  bj-sylget  34067  bj-alexim  34073  bj-cbvalimt  34085  bj-cbveximt  34086  bj-eqs  34121  bj-nnf-exlim  34200  bj-nnflemee  34207  bj-nnflemae  34208  bj-axc10  34220  bj-alequex  34221  bj-spimtv  34231  bj-spcimdv  34335  bj-spcimdvv  34336  sn-el  39402  2exim  41083  pm11.71  41101  onfrALTlem2  41252  19.41rg  41256  ax6e2nd  41264  elex2VD  41544  elex22VD  41545  onfrALTlem2VD  41595  19.41rgVD  41608  ax6e2eqVD  41613  ax6e2ndVD  41614  ax6e2ndeqVD  41615  ax6e2ndALT  41636  ax6e2ndeqALT  41637