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Theorem 19.23v 1855
Description: Special case of Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 28-Jun-1998.)
Assertion
Ref Expression
19.23v (∀𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓))
Distinct variable group:   𝜓,𝑥
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem 19.23v
StepHypRef Expression
1 ax-17 1506 . 2 (𝜓 → ∀𝑥𝜓)
2119.23h 1474 1 (∀𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104  wal 1329  wex 1468
This theorem was proved from axioms:  ax-mp 5  ax-gen 1425  ax-ie2 1470  ax-17 1506
This theorem is referenced by:  19.23vv  1856  2eu4  2092  gencbval  2734  euind  2871  reuind  2889  unissb  3766  disjnim  3920  dftr2  4028  ssrelrel  4639  cotr  4920  dffun2  5133  fununi  5191  dff13  5669  acexmidlem2  5771
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