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Theorem cbvriotavwOLD 7381
Description: Obsolete version of cbvriotavw 7380 as of 30-Sep-2024. (Contributed by NM, 18-Mar-2013.) (Revised by Gino Giotto, 26-Jan-2024.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
cbvriotavwOLD.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
cbvriotavwOLD (𝑥𝐴 𝜑) = (𝑦𝐴 𝜓)
Distinct variable groups:   𝑥,𝑦,𝐴   𝜑,𝑦   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑦)

Proof of Theorem cbvriotavwOLD
StepHypRef Expression
1 nfv 1910 . 2 𝑦𝜑
2 nfv 1910 . 2 𝑥𝜓
3 cbvriotavwOLD.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
41, 2, 3cbvriotaw 7379 1 (𝑥𝐴 𝜑) = (𝑦𝐴 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205   = wceq 1534  crio 7369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-11 2147  ax-12 2164  ax-ext 2698
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-tru 1537  df-ex 1775  df-nf 1779  df-sb 2061  df-clab 2705  df-cleq 2719  df-clel 2805  df-v 3471  df-in 3951  df-ss 3961  df-sn 4625  df-uni 4904  df-iota 6494  df-riota 7370
This theorem is referenced by: (None)
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