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Axiom ax-c11 32692
Description: Axiom ax-c11 32692 was the original version of ax-c11n 32693 ("n" for "new"), before it was discovered (in May 2008) that the shorter ax-c11n 32693 could replace it. It appears as Axiom scheme C11' 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This axiom is obsolete and should no longer be used.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 axc11 2197. (Contributed by NM, 10-May-1993.) (New usage is discouraged.)

Assertion
Ref Expression
ax-c11 (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑))

Detailed syntax breakdown of Axiom ax-c11
StepHypRef Expression
1 vx . . . 4 setvar 𝑥
2 vy . . . 4 setvar 𝑦
31, 2weq 1822 . . 3 wff 𝑥 = 𝑦
43, 1wal 1466 . 2 wff 𝑥 𝑥 = 𝑦
5 wph . . . 4 wff 𝜑
65, 1wal 1466 . . 3 wff 𝑥𝜑
75, 2wal 1466 . . 3 wff 𝑦𝜑
86, 7wi 4 . 2 wff (∀𝑥𝜑 → ∀𝑦𝜑)
94, 8wi 4 1 wff (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑))
Colors of variables: wff setvar class
This axiom is referenced by:  aecom-o  32704  hbae-o  32706  dral1-o  32707  axc11nfromc11  32730  dvelimf-o  32733
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