Axiom ax-9o 2138

Description: A variant of ax9 1949. 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This axiom is obsolete and should no longer be used.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 ax9o 1950. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.)

Assertion

Ref	Expression
ax-9o	⊢ (∀x(x = y → ∀xφ) → φ)

Detailed syntax breakdown of Axiom ax-9o

Step	Hyp	Ref	Expression
1		vx	. . . . 5 setvar x
2		vy	. . . . 5 setvar y
3	1, 2	weq 1643	. . . 4 wff x = y
4		wph	. . . . 5 wff φ
5	4, 1	wal 1540	. . . 4 wff ∀xφ
6	3, 5	wi 4	. . 3 wff (x = y → ∀xφ)
7	6, 1	wal 1540	. 2 wff ∀x(x = y → ∀xφ)
8	7, 4	wi 4	1 wff (∀x(x = y → ∀xφ) → φ)

This axiom is referenced by:  ax9from9o  2148  equid1  2158  equid1ALT  2176