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Theorem 19.23v 1779
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 1435 . 2 (𝜓 → ∀𝑥𝜓)
2119.23h 1403 1 (∀𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 102  wal 1257  wex 1397
This theorem was proved from axioms:  ax-mp 7  ax-gen 1354  ax-ie2 1399  ax-17 1435
This theorem is referenced by:  19.23vv  1780  2eu4  2009  gencbval  2619  euind  2751  reuind  2767  unissb  3638  dftr2  3884  ssrelrel  4468  cotr  4734  dffun2  4940  fununi  4995  dff13  5435  acexmidlem2  5537
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