Theorem exim 1758

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 1756	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1478  ∃wex 1701

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734

This theorem depends on definitions:  df-bi 197  df-ex 1702

This theorem is referenced by:  eximi  1759  19.38b  1765  19.23v  1899  nf5-1  2020  19.8a  2049  19.8aOLD  2050  19.9ht  2139  spimt  2252  elex2  3202  elex22  3203  vtoclegft  3266  spcimgft  3270  bj-axdd2  32215  bj-2exim  32234  bj-exlimh  32241  bj-alexim  32244  bj-sbex  32265  bj-alequexv  32294  bj-eqs  32302  bj-axc10  32346  bj-alequex  32347  bj-spimtv  32357  bj-spcimdv  32528  bj-spcimdvv  32529  2exim  38057  pm11.71  38076  onfrALTlem2  38240  19.41rg  38245  ax6e2nd  38253  elex2VD  38553  elex22VD  38554  onfrALTlem2VD  38605  19.41rgVD  38618  ax6e2eqVD  38623  ax6e2ndVD  38624  ax6e2ndeqVD  38625  ax6e2ndALT  38646  ax6e2ndeqALT  38647