Axiom ax-c10

Description: A variant of ax6 . 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This axiom is obsolete and should no longer be used.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 . (Contributed by NM, 10-Jan-1993) (New usage is discouraged.)

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

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		vx	⊢ 𝑥
1	0	cv	⊢ 𝑥
2		vy	⊢ 𝑦
3	2	cv	⊢ 𝑦
4	1 3	wceq	⊢ 𝑥 = 𝑦
5		wph	⊢ 𝜑
6	5 0	wal	⊢ ∀ 𝑥 𝜑
7	4 6	wi	⊢ ( 𝑥 = 𝑦 → ∀ 𝑥 𝜑 )
8	7 0	wal	⊢ ∀ 𝑥 ( 𝑥 = 𝑦 → ∀ 𝑥 𝜑 )
9	8 5	wi	⊢ ( ∀ 𝑥 ( 𝑥 = 𝑦 → ∀ 𝑥 𝜑 ) → 𝜑 )