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Theorem axc7e 2129
Description: Abbreviated version of axc7 2128 using the existential quantifier. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
axc7e (∃𝑥𝑥𝜑𝜑)

Proof of Theorem axc7e
StepHypRef Expression
1 hbe1a 2019 . 2 (∃𝑥𝑥𝜑 → ∀𝑥𝜑)
2 sp 2051 . 2 (∀𝑥𝜑𝜑)
31, 2syl 17 1 (∃𝑥𝑥𝜑𝜑)
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  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-12 2044
This theorem depends on definitions:  df-bi 197  df-ex 1702
This theorem is referenced by:  19.9ht  2139  bj-axc10  32402
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