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Mirrors > Home > MPE Home > Th. List > ax13w | Structured version Visualization version GIF version |
Description: Weak version (principal instance) of ax-13 2137. (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 1953, ax11w 1954, and ax12w 1957. (Contributed by NM, 10-Apr-2017.) |
Ref | Expression |
---|---|
ax13w | ⊢ (¬ 𝑥 = 𝑦 → (𝑦 = 𝑧 → ∀𝑥 𝑦 = 𝑧)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax5d 1790 | 1 ⊢ (¬ 𝑥 = 𝑦 → (𝑦 = 𝑧 → ∀𝑥 𝑦 = 𝑧)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1466 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-5 1789 |
This theorem is referenced by: (None) |
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