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Theorem chvarv 1914
 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 1837 . 2 (∀𝑥𝜑𝜓)
3 chv.2 . 2 𝜑
42, 3mpg 1428 1 𝜓
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 104 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511 This theorem depends on definitions:  df-bi 116  df-nf 1438 This theorem is referenced by:  axext3  2137  axsep2  4079  tz6.12f  5490  ltordlem  8336  bdsep2  13399  strcoll2  13496
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