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Theorem ax13dgen3 2183
Description: Degenerate instance of ax-13 2354 where bundled variables 𝑦 and 𝑧 have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017.)
Assertion
Ref Expression
ax13dgen3 𝑥 = 𝑦 → (𝑦 = 𝑦 → ∀𝑥 𝑦 = 𝑦))

Proof of Theorem ax13dgen3
StepHypRef Expression
1 equid 2111 . . 3 𝑦 = 𝑦
21ax-gen 1891 . 2 𝑥 𝑦 = 𝑦
322a1i 12 1 𝑥 = 𝑦 → (𝑦 = 𝑦 → ∀𝑥 𝑦 = 𝑦))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1651
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107
This theorem depends on definitions:  df-bi 199  df-ex 1876
This theorem is referenced by: (None)
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