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Theorem eubiOLD 42808
Description: Obsolete proof of eubi 2579 as of 7-Oct-2022. (Contributed by Andrew Salmon, 11-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
eubiOLD (∀𝑥(𝜑𝜓) → (∃!𝑥𝜑 ↔ ∃!𝑥𝜓))

Proof of Theorem eubiOLD
StepHypRef Expression
1 nfa1 2149 . 2 𝑥𝑥(𝜑𝜓)
2 sp 2177 . 2 (∀𝑥(𝜑𝜓) → (𝜑𝜓))
31, 2eubid 2582 1 (∀𝑥(𝜑𝜓) → (∃!𝑥𝜑 ↔ ∃!𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wal 1540  ∃!weu 2563
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-10 2138  ax-12 2172
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-ex 1783  df-nf 1787  df-mo 2535  df-eu 2564
This theorem is referenced by: (None)
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