Theorem exim 1761

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 1759	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1481  ∃wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by:  eximi  1762  19.38b  1768  19.23v  1902  nf5-1  2023  19.8a  2052  19.9ht  2143  spimt  2253  elex2  3216  elex22  3217  vtoclegft  3280  spcimgft  3284  bj-axdd2  32576  bj-2exim  32595  bj-exlimh  32602  bj-alexim  32605  bj-sbex  32626  bj-alequexv  32655  bj-eqs  32663  bj-axc10  32707  bj-alequex  32708  bj-spimtv  32718  bj-spcimdv  32884  bj-spcimdvv  32885  2exim  38578  pm11.71  38597  onfrALTlem2  38761  19.41rg  38766  ax6e2nd  38774  elex2VD  39073  elex22VD  39074  onfrALTlem2VD  39125  19.41rgVD  39138  ax6e2eqVD  39143  ax6e2ndVD  39144  ax6e2ndeqVD  39145  ax6e2ndALT  39166  ax6e2ndeqALT  39167