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Axiom ax-c10 33064
Description: A variant of ax6 2142. Axiom scheme C10' in [Megill] p. 448 (p. 16 of the preprint).

This axiom is obsolete and should no longer be used. It is proved above as theorem axc10 2143. (Contributed by NM, 10-Jan-1993.) (New usage is discouraged.)

Assertion
Ref Expression
ax-c10 (∀𝑥(𝑥 = 𝑦 → ∀𝑥𝜑) → 𝜑)

Detailed syntax breakdown of Axiom ax-c10
StepHypRef Expression
1 vx . . . . 5 setvar 𝑥
2 vy . . . . 5 setvar 𝑦
31, 2weq 1824 . . . 4 wff 𝑥 = 𝑦
4 wph . . . . 5 wff 𝜑
54, 1wal 1472 . . . 4 wff 𝑥𝜑
63, 5wi 4 . . 3 wff (𝑥 = 𝑦 → ∀𝑥𝜑)
76, 1wal 1472 . 2 wff 𝑥(𝑥 = 𝑦 → ∀𝑥𝜑)
87, 4wi 4 1 wff (∀𝑥(𝑥 = 𝑦 → ∀𝑥𝜑) → 𝜑)
Colors of variables: wff setvar class
This axiom is referenced by:  ax6fromc10  33074  equid1  33077  equid1ALT  33103
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