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Theorem 19.2 1878
Description: Theorem 19.2 of [Margaris] p. 89. This corresponds to the axiom (D) of modal logic. Note: This proof is very different from Margaris' because we only have Tarski's FOL axiom schemes available at this point. See the later 19.2g 2044 for a more conventional proof of a more general result, which uses additional axioms. (Contributed by NM, 2-Aug-2017.) Remove dependency on ax-7 1921. (Revised by Wolf Lammen, 4-Dec-2017.)
Assertion
Ref Expression
19.2 (∀𝑥𝜑 → ∃𝑥𝜑)

Proof of Theorem 19.2
StepHypRef Expression
1 id 22 . . 3 (𝜑𝜑)
21exiftru 1877 . 2 𝑥(𝜑𝜑)
3219.35i 1794 1 (∀𝑥𝜑 → ∃𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1472  wex 1694
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-6 1874
This theorem depends on definitions:  df-bi 195  df-ex 1695
This theorem is referenced by:  19.2d  1879  19.39  1885  19.24  1886  19.34  1887  eusv2i  4784  extt  31379  bj-ax6e  31648  bj-spnfw  31651  bj-modald  31654  wl-speqv  32290  wl-19.8eqv  32291  pm10.251  37384  ax6e2eq  37597  ax6e2eqVD  37968
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