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Theorem eximdh 1543
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 1399 . 2 (𝜑 → ∀𝑥(𝜓𝜒))
4 exim 1531 . 2 (∀𝑥(𝜓𝜒) → (∃𝑥𝜓 → ∃𝑥𝜒))
53, 4syl 14 1 (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1283  wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  eximd  1544  19.41h  1616  hbexd  1625  equsex  1657  equsexd  1658  spimeh  1668  sbiedh  1711  exdistrfor  1722  eximdv  1802  cbvexdh  1843  mopick2  2025  2euex  2029  bj-sbimedh  10733
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