Theorem exim 1836

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 1834	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1537  ∃wex 1782

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812

This theorem depends on definitions:  df-bi 206  df-ex 1783

This theorem is referenced by:  eximi  1837  19.38b  1843  19.23v  1945  alequexv  2004  nf5-1  2141  spimt  2386  darii  2666  festino  2675  baroco  2677  darapti  2685  elex2OLD  3453  elex22  3454  vtoclegft  3522  spcimgft  3526  rspn0  4286  bj-axdd2  34774  bj-2exim  34793  bj-sylget  34802  bj-alexim  34808  bj-cbvalimt  34820  bj-cbveximt  34821  bj-eqs  34856  bj-nnf-exlim  34938  bj-nnflemee  34945  bj-nnflemae  34946  bj-axc10  34965  bj-alequex  34966  bj-spimtv  34976  bj-spcimdv  35080  bj-spcimdvv  35081  sn-el  40187  2exim  41997  pm11.71  42015  onfrALTlem2  42166  19.41rg  42170  ax6e2nd  42178  elex2VD  42458  elex22VD  42459  onfrALTlem2VD  42509  19.41rgVD  42522  ax6e2eqVD  42527  ax6e2ndVD  42528  ax6e2ndeqVD  42529  ax6e2ndALT  42550  ax6e2ndeqALT  42551