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Theorem chvarv 1812
 Description: Implicit substitution of 𝑦 for 𝑥 into a theorem. (Contributed by NM, 20-Apr-1994.)
Hypotheses
Ref Expression
chv.1 (𝑥 = 𝑦 → (𝜑𝜓))
chv.2 𝜑
Assertion
Ref Expression
chvarv 𝜓
Distinct variable group:   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝜓(𝑦)

Proof of Theorem chvarv
StepHypRef Expression
1 chv.1 . . 3 (𝑥 = 𝑦 → (𝜑𝜓))
21spv 1740 . 2 (∀𝑥𝜑𝜓)
3 chv.2 . 2 𝜑
42, 3mpg 1340 1 𝜓
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427 This theorem depends on definitions:  df-bi 110  df-nf 1350 This theorem is referenced by:  axext3  2023  axsep2  3876  tz6.12f  5202  tfrlem3-2  5927  bdsep2  10006  strcoll2  10108
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