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Theorem reuanidOLD 3383
Description: Obsolete version of reuanid 3381 as of 12-Jan-2025. (Contributed by Peter Mazsa, 12-Feb-2018.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
reuanidOLD (∃!𝑥𝐴 (𝑥𝐴𝜑) ↔ ∃!𝑥𝐴 𝜑)

Proof of Theorem reuanidOLD
StepHypRef Expression
1 anabs5 660 . . 3 ((𝑥𝐴 ∧ (𝑥𝐴𝜑)) ↔ (𝑥𝐴𝜑))
21eubii 2573 . 2 (∃!𝑥(𝑥𝐴 ∧ (𝑥𝐴𝜑)) ↔ ∃!𝑥(𝑥𝐴𝜑))
3 df-reu 3371 . 2 (∃!𝑥𝐴 (𝑥𝐴𝜑) ↔ ∃!𝑥(𝑥𝐴 ∧ (𝑥𝐴𝜑)))
4 df-reu 3371 . 2 (∃!𝑥𝐴 𝜑 ↔ ∃!𝑥(𝑥𝐴𝜑))
52, 3, 43bitr4i 303 1 (∃!𝑥𝐴 (𝑥𝐴𝜑) ↔ ∃!𝑥𝐴 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 205  wa 395  wcel 2098  ∃!weu 2556  ∃!wreu 3368
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1774  df-mo 2528  df-eu 2557  df-reu 3371
This theorem is referenced by: (None)
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