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Theorem ax8v 2115
Description: Weakened version of ax-8 2114, with a disjoint variable condition on 𝑥, 𝑦. This should be the only proof referencing ax-8 2114, and it should be referenced only by its two weakened versions ax8v1 2116 and ax8v2 2117, from which ax-8 2114 is then rederived as ax8 2118, which shows that either ax8v 2115 or the conjunction of ax8v1 2116 and ax8v2 2117 is sufficient. (Contributed by BJ, 7-Dec-2020.) Use ax8 2118 instead. (New usage is discouraged.)
Ref Expression
ax8v (𝑥 = 𝑦 → (𝑥𝑧𝑦𝑧))
Distinct variable group:   𝑥,𝑦

Proof of Theorem ax8v
StepHypRef Expression
1 ax-8 2114 1 (𝑥 = 𝑦 → (𝑥𝑧𝑦𝑧))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-8 2114
This theorem is referenced by:  ax8v1  2116  ax8v2  2117
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