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Theorem eximdh 1788
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 . 2 (𝜑 → ∀𝑥𝜑)
2 eximdh.2 . . 3 (𝜑 → (𝜓𝜒))
32aleximi 1756 . 2 (∀𝑥𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))
41, 3syl 17 1 (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478  wex 1701
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734
This theorem depends on definitions:  df-bi 197  df-ex 1702
This theorem is referenced by:  eximdv  1843  eximd  2083  eximdOLD  2196  ax6e2eq  38282
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