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Theorem chvarv 2405
Description: Implicit substitution of 𝑦 for 𝑥 into a theorem. (Contributed by NM, 20-Apr-1994.) (Proof shortened by Wolf Lammen, 22-Apr-2018.)
Hypotheses
Ref Expression
chvarv.1 (𝑥 = 𝑦 → (𝜑𝜓))
chvarv.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 nfv 1906 . 2 𝑥𝜓
2 chvarv.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
3 chvarv.2 . 2 𝜑
41, 2, 3chvar 2404 1 𝜓
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-12 2167  ax-13 2381
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772  df-nf 1776
This theorem is referenced by:  bnj1326  32195  vonioo  42841  vonicc  42844
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