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Theorem eximdh 1604
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 20-May-1996.)
Hypotheses
Ref Expression
eximdh.1 (𝜑 → ∀𝑥𝜑)
eximdh.2 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
eximdh (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))

Proof of Theorem eximdh
StepHypRef Expression
1 eximdh.1 . . 3 (𝜑 → ∀𝑥𝜑)
2 eximdh.2 . . 3 (𝜑 → (𝜓𝜒))
31, 2alrimih 1462 . 2 (𝜑 → ∀𝑥(𝜓𝜒))
4 exim 1592 . 2 (∀𝑥(𝜓𝜒) → (∃𝑥𝜓 → ∃𝑥𝜒))
53, 4syl 14 1 (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1346  wex 1485
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  eximd  1605  19.41h  1678  hbexd  1687  equsex  1721  equsexd  1722  spimeh  1732  sbiedh  1780  exdistrfor  1793  eximdv  1873  cbvexdh  1919  mopick2  2102  2euex  2106  bj-sbimedh  13806
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