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Theorem exlimexi 44436
Description: Inference similar to Theorem 19.23 of [Margaris] p. 90. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
exlimexi.1 (𝜓 → ∀𝑥𝜓)
exlimexi.2 (∃𝑥𝜑 → (𝜑𝜓))
Assertion
Ref Expression
exlimexi (∃𝑥𝜑𝜓)

Proof of Theorem exlimexi
StepHypRef Expression
1 hbe1 2138 . . 3 (∃𝑥𝜑 → ∀𝑥𝑥𝜑)
2 exlimexi.1 . . 3 (𝜓 → ∀𝑥𝜓)
3 exlimexi.2 . . 3 (∃𝑥𝜑 → (𝜑𝜓))
41, 2, 3exlimdh 2288 . 2 (∃𝑥𝜑 → (∃𝑥𝜑𝜓))
54pm2.43i 52 1 (∃𝑥𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1535  wex 1777
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-10 2136  ax-12 2173
This theorem depends on definitions:  df-bi 207  df-ex 1778  df-nf 1782
This theorem is referenced by:  sb5ALT  44437  exinst  44536
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