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Theorem euequOLD 2618
 Description: Obsolete proof of euequ 2617 as of 28-Feb-2023. (Contributed by Stefan Allan, 4-Dec-2008.) (Proof shortened by Wolf Lammen, 8-Sep-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
euequOLD ∃!𝑥 𝑥 = 𝑦
Distinct variable group:   𝑥,𝑦

Proof of Theorem euequOLD
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 ax6evr 1973 . . 3 𝑧 𝑦 = 𝑧
2 equequ2 1984 . . . 4 (𝑦 = 𝑧 → (𝑥 = 𝑦𝑥 = 𝑧))
32alrimiv 1887 . . 3 (𝑦 = 𝑧 → ∀𝑥(𝑥 = 𝑦𝑥 = 𝑧))
41, 3eximii 1800 . 2 𝑧𝑥(𝑥 = 𝑦𝑥 = 𝑧)
5 eu6 2591 . 2 (∃!𝑥 𝑥 = 𝑦 ↔ ∃𝑧𝑥(𝑥 = 𝑦𝑥 = 𝑧))
64, 5mpbir 223 1 ∃!𝑥 𝑥 = 𝑦
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 198  ∀wal 1506  ∃wex 1743  ∃!weu 2584 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1759  ax-4 1773  ax-5 1870  ax-6 1929  ax-7 1966  ax-10 2080  ax-12 2107 This theorem depends on definitions:  df-bi 199  df-an 388  df-or 835  df-ex 1744  df-nf 1748  df-mo 2548  df-eu 2585 This theorem is referenced by: (None)
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