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Theorem eubiOLD 44432
Description: Obsolete proof of eubi 2582 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 2181 . 2 (∀𝑥(𝜑𝜓) → (𝜑𝜓))
31, 2eubid 2585 1 (∀𝑥(𝜑𝜓) → (∃!𝑥𝜑 ↔ ∃!𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206  wal 1535  ∃!weu 2566
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-10 2139  ax-12 2175
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-ex 1777  df-nf 1781  df-mo 2538  df-eu 2567
This theorem is referenced by: (None)
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