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Axiom ax-c11 33649
Description: Axiom ax-c11 33649 was the original version of ax-c11n 33650 ("n" for "new"), before it was discovered (in May 2008) that the shorter ax-c11n 33650 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This axiom is obsolete and should no longer be used.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 2313. (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 1871 . . 3 wff 𝑥 = 𝑦
43, 1wal 1478 . 2 wff 𝑥 𝑥 = 𝑦
5 wph . . . 4 wff 𝜑
65, 1wal 1478 . . 3 wff 𝑥𝜑
75, 2wal 1478 . . 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  33663  hbae-o  33665  dral1-o  33666  axc11nfromc11  33688  dvelimf-o  33691
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