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Theorem eexinst11 37754
 Description: exinst11 37872 without virtual deductions. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eexinst11.1 (𝜑 → ∃𝑥𝜓)
eexinst11.2 (𝜑 → (𝜓𝜒))
eexinst11.3 (𝜑 → ∀𝑥𝜑)
eexinst11.4 (𝜒 → ∀𝑥𝜒)
Assertion
Ref Expression
eexinst11 (𝜑𝜒)

Proof of Theorem eexinst11
StepHypRef Expression
1 eexinst11.1 . . 3 (𝜑 → ∃𝑥𝜓)
2 eexinst11.3 . . . 4 (𝜑 → ∀𝑥𝜑)
3 eexinst11.4 . . . 4 (𝜒 → ∀𝑥𝜒)
4 eexinst11.2 . . . 4 (𝜑 → (𝜓𝜒))
52, 3, 4exlimdh 2134 . . 3 (𝜑 → (∃𝑥𝜓𝜒))
61, 5syl5com 31 . 2 (𝜑 → (𝜑𝜒))
76pm2.43i 50 1 (𝜑𝜒)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1473  ∃wex 1695 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034 This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nf 1701 This theorem is referenced by:  vk15.4j  37755  exinst11  37872
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