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Theorem cbvex2vOLD 2287
 Description: Obsolete proof of cbvex2v 2286 as of 18-Jul-2021. (Contributed by NM, 26-Jul-1995.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
cbval2v.1 ((𝑥 = 𝑧𝑦 = 𝑤) → (𝜑𝜓))
Assertion
Ref Expression
cbvex2vOLD (∃𝑥𝑦𝜑 ↔ ∃𝑧𝑤𝜓)
Distinct variable groups:   𝑧,𝑤,𝜑   𝑥,𝑦,𝜓   𝑥,𝑤   𝑦,𝑧
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝜓(𝑧,𝑤)

Proof of Theorem cbvex2vOLD
StepHypRef Expression
1 nfv 1840 . 2 𝑧𝜑
2 nfv 1840 . 2 𝑤𝜑
3 nfv 1840 . 2 𝑥𝜓
4 nfv 1840 . 2 𝑦𝜓
5 cbval2v.1 . 2 ((𝑥 = 𝑧𝑦 = 𝑤) → (𝜑𝜓))
61, 2, 3, 4, 5cbvex2 2279 1 (∃𝑥𝑦𝜑 ↔ ∃𝑧𝑤𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196   ∧ wa 384  ∃wex 1701 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1702  df-nf 1707 This theorem is referenced by: (None)
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