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Theorem 2eu2ex 2528
Description: Double existential uniqueness. (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2eu2ex (∃!𝑥∃!𝑦𝜑 → ∃𝑥𝑦𝜑)

Proof of Theorem 2eu2ex
StepHypRef Expression
1 euex 2476 . 2 (∃!𝑥∃!𝑦𝜑 → ∃𝑥∃!𝑦𝜑)
2 euex 2476 . . 3 (∃!𝑦𝜑 → ∃𝑦𝜑)
32eximi 1750 . 2 (∃𝑥∃!𝑦𝜑 → ∃𝑥𝑦𝜑)
41, 3syl 17 1 (∃!𝑥∃!𝑦𝜑 → ∃𝑥𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1694  ∃!weu 2452
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873
This theorem depends on definitions:  df-bi 195  df-ex 1695  df-eu 2456
This theorem is referenced by:  2eu1  2535
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