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Theorem cbvreuvwOLD 3412
Description: Obsolete version of cbvreuvw 3399 as of 30-Sep-2024. (Contributed by NM, 5-Apr-2004.) (Revised by Gino Giotto, 10-Jan-2024.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
cbvreuvwOLD.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
cbvreuvwOLD (∃!𝑥𝐴 𝜑 ↔ ∃!𝑦𝐴 𝜓)
Distinct variable groups:   𝑥,𝑦,𝐴   𝜑,𝑦   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑦)

Proof of Theorem cbvreuvwOLD
StepHypRef Expression
1 nfv 1916 . 2 𝑦𝜑
2 nfv 1916 . 2 𝑥𝜓
3 cbvreuvwOLD.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
41, 2, 3cbvreuw 3405 1 (∃!𝑥𝐴 𝜑 ↔ ∃!𝑦𝐴 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  ∃!wreu 3373
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-11 2153  ax-12 2170
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1543  df-ex 1781  df-nf 1785  df-mo 2533  df-eu 2562  df-clel 2809  df-nfc 2884  df-ral 3061  df-rex 3070  df-rmo 3375  df-reu 3376
This theorem is referenced by: (None)
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