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Theorem 19.37v 1966
Description: Version of 19.37 2138 with a dv condition, requiring fewer axioms. (Contributed by NM, 21-Jun-1993.)
Assertion
Ref Expression
19.37v (∃𝑥(𝜑𝜓) ↔ (𝜑 → ∃𝑥𝜓))
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem 19.37v
StepHypRef Expression
1 19.35 1845 . 2 (∃𝑥(𝜑𝜓) ↔ (∀𝑥𝜑 → ∃𝑥𝜓))
2 19.3v 1954 . . 3 (∀𝑥𝜑𝜑)
32imbi1i 338 . 2 ((∀𝑥𝜑 → ∃𝑥𝜓) ↔ (𝜑 → ∃𝑥𝜓))
41, 3bitri 264 1 (∃𝑥(𝜑𝜓) ↔ (𝜑 → ∃𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1521  wex 1744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945
This theorem depends on definitions:  df-bi 197  df-ex 1745
This theorem is referenced by:  19.37ivOLD  1967  eqvincg  3360  axrep5  4809  fvn0ssdmfun  6390  kmlem14  9023  kmlem15  9024  bnj132  30920  bnj1098  30980  bnj150  31072  bnj865  31119  bnj996  31151  bnj1021  31160  bnj1090  31173  bnj1176  31199  bj-axrep5  32917  cnvssco  38229  refimssco  38230  19.37vv  38901  pm11.61  38910  relopabVD  39451  rmoanim  41500
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