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Mirrors > Home > MPE Home > Th. List > ax8v | Structured version Visualization version GIF version |
Description: Weakened version of ax-8 2107, with a disjoint variable condition on 𝑥, 𝑦. This should be the only proof referencing ax-8 2107, and it should be referenced only by its two weakened versions ax8v1 2109 and ax8v2 2110, from which ax-8 2107 is then rederived as ax8 2111, which shows that either ax8v 2108 or the conjunction of ax8v1 2109 and ax8v2 2110 is sufficient. (Contributed by BJ, 7-Dec-2020.) Use ax8 2111 instead. (New usage is discouraged.) |
Ref | Expression |
---|---|
ax8v | ⊢ (𝑥 = 𝑦 → (𝑥 ∈ 𝑧 → 𝑦 ∈ 𝑧)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-8 2107 | 1 ⊢ (𝑥 = 𝑦 → (𝑥 ∈ 𝑧 → 𝑦 ∈ 𝑧)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-8 2107 |
This theorem is referenced by: ax8v1 2109 ax8v2 2110 |
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