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Description: Theorem 19.2 of Margaris p. 89. This corresponds to the axiom (D) of modal logic (the other standard formulation being extru ). 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 for a more conventional proof of a more general result, which uses additional axioms. The reverse implication is the defining property of effective nonfreeness (see df-nf ). (Contributed by NM, 2-Aug-2017) Remove dependency on ax-7 . (Revised by Wolf Lammen, 4-Dec-2017)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | 19.2 | |- ( A. x ph -> E. x ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | id | |- ( ph -> ph ) |
|
| 2 | 1 | exgen | |- E. x ( ph -> ph ) |
| 3 | 2 | 19.35i | |- ( A. x ph -> E. x ph ) |