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Axiom ax-8d 30396
Description: Distinct variable version of ax-7 1922. (Contributed by Mario Carneiro, 14-Aug-2015.)
Assertion
Ref Expression
ax-8d (𝑥 = 𝑦 → (𝑥 = 𝑧𝑦 = 𝑧))
Distinct variable group:   𝑥,𝑦,𝑧

Detailed syntax breakdown of Axiom ax-8d
StepHypRef Expression
1 vx . . 3 setvar 𝑥
2 vy . . 3 setvar 𝑦
31, 2weq 1861 . 2 wff 𝑥 = 𝑦
4 vz . . . 4 setvar 𝑧
51, 4weq 1861 . . 3 wff 𝑥 = 𝑧
62, 4weq 1861 . . 3 wff 𝑦 = 𝑧
75, 6wi 4 . 2 wff (𝑥 = 𝑧𝑦 = 𝑧)
83, 7wi 4 1 wff (𝑥 = 𝑦 → (𝑥 = 𝑧𝑦 = 𝑧))
Colors of variables: wff setvar class
This axiom is referenced by: (None)
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