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Theorem axc7e 2297
Description: Abbreviated version of axc7 2296 using the existential quantifier. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 8-Jul-2022.)
Assertion
Ref Expression
axc7e (∃𝑥𝑥𝜑𝜑)

Proof of Theorem axc7e
StepHypRef Expression
1 hbe1a 2177 . 2 (∃𝑥𝑥𝜑 → ∀𝑥𝜑)
2119.21bi 2213 1 (∃𝑥𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1629  wex 1852
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-10 2174  ax-12 2203
This theorem depends on definitions:  df-bi 197  df-ex 1853
This theorem is referenced by:  19.9ht  2308  bj-axc10  33044
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