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Theorem r19.37av 2480
Description: Restricted version of one direction of Theorem 19.37 of [Margaris] p. 90. (Contributed by NM, 2-Apr-2004.)
Assertion
Ref Expression
r19.37av (∃𝑥𝐴 (𝜑𝜓) → (𝜑 → ∃𝑥𝐴 𝜓))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝐴(𝑥)

Proof of Theorem r19.37av
StepHypRef Expression
1 nfv 1437 . 2 𝑥𝜑
21r19.37 2479 1 (∃𝑥𝐴 (𝜑𝜓) → (𝜑 → ∃𝑥𝐴 𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wrex 2324
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-17 1435  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-ral 2328  df-rex 2329
This theorem is referenced by:  ssiun  3727
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