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Theorem 19.23v 1811
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 1464 . 2 (𝜓 → ∀𝑥𝜓)
2119.23h 1432 1 (∀𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103  wal 1287  wex 1426
This theorem was proved from axioms:  ax-mp 7  ax-gen 1383  ax-ie2 1428  ax-17 1464
This theorem is referenced by:  19.23vv  1812  2eu4  2041  gencbval  2667  euind  2802  reuind  2820  unissb  3683  disjnim  3836  dftr2  3938  ssrelrel  4538  cotr  4813  dffun2  5025  fununi  5082  dff13  5547  acexmidlem2  5649
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