Theorem exim 1830

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 1828	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1531  ∃wex 1776

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806

This theorem depends on definitions:  df-bi 209  df-ex 1777

This theorem is referenced by:  eximi  1831  19.38b  1837  19.23v  1939  alequexv  2003  spsbeOLD  2085  nf5-1  2145  spimt  2400  darii  2748  festino  2757  baroco  2759  darapti  2767  elex2  3517  elex22  3518  vtoclegft  3582  spcimgft  3586  bj-axdd2  33921  bj-2exim  33940  bj-sylget  33949  bj-alexim  33955  bj-cbvalimt  33967  bj-cbveximt  33968  bj-eqs  34003  bj-nnf-exlim  34080  bj-nnflemee  34087  bj-nnflemae  34088  bj-axc10  34100  bj-alequex  34101  bj-spimtv  34111  bj-spcimdv  34206  bj-spcimdvv  34207  sn-el  39103  2exim  40704  pm11.71  40722  onfrALTlem2  40873  19.41rg  40877  ax6e2nd  40885  elex2VD  41165  elex22VD  41166  onfrALTlem2VD  41216  19.41rgVD  41229  ax6e2eqVD  41234  ax6e2ndVD  41235  ax6e2ndeqVD  41236  ax6e2ndALT  41257  ax6e2ndeqALT  41258