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Theorem chvarv 1857
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 1785 . 2 (∀𝑥𝜑𝜓)
3 chv.2 . 2 𝜑
42, 3mpg 1383 1 𝜓
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470
This theorem depends on definitions:  df-bi 115  df-nf 1393
This theorem is referenced by:  axext3  2068  axsep2  3931  tz6.12f  5289  bdsep2  11206  strcoll2  11307
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