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Theorem eximd 1519
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
eximd.1 𝑥𝜑
eximd.2 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
eximd (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))

Proof of Theorem eximd
StepHypRef Expression
1 eximd.1 . . 3 𝑥𝜑
21nfri 1428 . 2 (𝜑 → ∀𝑥𝜑)
3 eximd.2 . 2 (𝜑 → (𝜓𝜒))
42, 3eximdh 1518 1 (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1365  wex 1397
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-ial 1443
This theorem depends on definitions:  df-bi 114  df-nf 1366
This theorem is referenced by:  19.41  1592  mo2icl  2743  copsexg  4009  ssopab2  4040  eunex  4313  spc2ed  5882
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