Theorem exim 1837

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 1835	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1537  ∃wex 1783

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813

This theorem depends on definitions:  df-bi 206  df-ex 1784

This theorem is referenced by:  eximi  1838  19.38b  1844  19.23v  1946  alequexv  2005  nf5-1  2143  spimt  2386  darii  2666  festino  2675  baroco  2677  darapti  2685  elex2  3443  elex22  3444  vtoclegft  3512  spcimgft  3516  rspn0  4283  bj-axdd2  34701  bj-2exim  34720  bj-sylget  34729  bj-alexim  34735  bj-cbvalimt  34747  bj-cbveximt  34748  bj-eqs  34783  bj-nnf-exlim  34865  bj-nnflemee  34872  bj-nnflemae  34873  bj-axc10  34892  bj-alequex  34893  bj-spimtv  34903  bj-spcimdv  35007  bj-spcimdvv  35008  sn-el  40115  2exim  41886  pm11.71  41904  onfrALTlem2  42055  19.41rg  42059  ax6e2nd  42067  elex2VD  42347  elex22VD  42348  onfrALTlem2VD  42398  19.41rgVD  42411  ax6e2eqVD  42416  ax6e2ndVD  42417  ax6e2ndeqVD  42418  ax6e2ndALT  42439  ax6e2ndeqALT  42440