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Theorem axi10 2581
Description: Axiom of Quantifier Substitution (intuitionistic logic axiom ax-10). This is just axc11n 2289 by another name. (Contributed by Jim Kingdon, 31-Dec-2017.) (New usage is discouraged.)
Assertion
Ref Expression
axi10 (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥)

Proof of Theorem axi10
StepHypRef Expression
1 axc11n 2289 1 (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-10 2004  ax-12 2031  ax-13 2227
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700
This theorem is referenced by: (None)
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