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Theorem ax13w 1999
Description: Weak version (principal instance) of ax-13 2233. (Because 𝑦 and 𝑧 don't need to be distinct, this actually bundles the principal instance and the degenerate instance 𝑥 = 𝑦 → (𝑦 = 𝑦 → ∀𝑥𝑦 = 𝑦)).) Uses only Tarski's FOL axiom schemes. The proof is trivial but is included to complete the set ax10w 1992, ax11w 1993, and ax12w 1996. (Contributed by NM, 10-Apr-2017.)
Assertion
Ref Expression
ax13w 𝑥 = 𝑦 → (𝑦 = 𝑧 → ∀𝑥 𝑦 = 𝑧))
Distinct variable groups:   𝑥,𝑦   𝑥,𝑧

Proof of Theorem ax13w
StepHypRef Expression
1 ax5d 1827 1 𝑥 = 𝑦 → (𝑦 = 𝑧 → ∀𝑥 𝑦 = 𝑧))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-5 1826
This theorem is referenced by: (None)
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