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Theorem chvarv 2410
Description: Implicit substitution of 𝑦 for 𝑥 into a theorem. Usage of this theorem is discouraged because it depends on ax-13 2386. Use the weaker chvarvv 2001 if possible. (Contributed by NM, 20-Apr-1994.) (Proof shortened by Wolf Lammen, 22-Apr-2018.) (New usage is discouraged.)
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 1911 . 2 𝑥𝜓
2 chvarv.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
3 chvarv.2 . 2 𝜑
41, 2, 3chvar 2409 1 𝜓
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 208
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-12 2173  ax-13 2386
This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1777  df-nf 1781
This theorem is referenced by: (None)
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