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Theorem ax13dgen1 2168
Description: Degenerate instance of ax-13 2407 where bundled variables 𝑥 and 𝑦 have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017.)
Assertion
Ref Expression
ax13dgen1 𝑥 = 𝑥 → (𝑥 = 𝑧 → ∀𝑥 𝑥 = 𝑧))

Proof of Theorem ax13dgen1
StepHypRef Expression
1 equid 2096 . 2 𝑥 = 𝑥
21pm2.24i 147 1 𝑥 = 𝑥 → (𝑥 = 𝑧 → ∀𝑥 𝑥 = 𝑧))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1628
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092
This theorem depends on definitions:  df-bi 197  df-ex 1852
This theorem is referenced by:  ax13dgen4OLD  2172
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