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Theorem eexinst11 39253
Description: exinst11 39371 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 2296 . . 3 (𝜑 → (∃𝑥𝜓𝜒))
61, 5syl5com 31 . 2 (𝜑 → (𝜑𝜒))
76pm2.43i 52 1 (𝜑𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1630  wex 1853
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-10 2168  ax-12 2196
This theorem depends on definitions:  df-bi 197  df-ex 1854  df-nf 1859
This theorem is referenced by:  vk15.4j  39254  exinst11  39371
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