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Theorem ax9v 2123
Description: Weakened version of ax-9 2122, with a disjoint variable condition on 𝑥, 𝑦. This should be the only proof referencing ax-9 2122, and it should be referenced only by its two weakened versions ax9v1 2124 and ax9v2 2125, from which ax-9 2122 is then rederived as ax9 2126, which shows that either ax9v 2123 or the conjunction of ax9v1 2124 and ax9v2 2125 is sufficient. (Contributed by BJ, 7-Dec-2020.) Use ax9 2126 instead. (New usage is discouraged.)
Ref Expression
ax9v (𝑥 = 𝑦 → (𝑧𝑥𝑧𝑦))
Distinct variable group:   𝑥,𝑦

Proof of Theorem ax9v
StepHypRef Expression
1 ax-9 2122 1 (𝑥 = 𝑦 → (𝑧𝑥𝑧𝑦))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-9 2122
This theorem is referenced by:  ax9v1  2124  ax9v2  2125
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