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Theorem chvarvOLD 2341
 Description: Obsolete proof of chvarv 2340 as of 14-Jul-2021. (Contributed by NM, 20-Apr-1994.) (Proof shortened by Wolf Lammen, 22-Apr-2018.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
chvarv.1 (𝑥 = 𝑦 → (𝜑𝜓))
chvarv.2 𝜑
Assertion
Ref Expression
chvarvOLD 𝜓
Distinct variable group:   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝜓(𝑦)

Proof of Theorem chvarvOLD
StepHypRef Expression
1 nfv 1924 . 2 𝑥𝜓
2 chvarv.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
3 chvarv.2 . 2 𝜑
41, 2, 3chvar 2339 1 𝜓
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1818  ax-5 1920  ax-6 1986  ax-7 2022  ax-12 2128  ax-13 2323 This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1786  df-nf 1791 This theorem is referenced by: (None)
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