Axiom ax-10o 2139

Description: Axiom ax-10o 2139 ("o" for "old") was the original version of ax-10 2140, before it was discovered (in May 2008) that the shorter ax-10 2140 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This axiom is obsolete and should no longer be used.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 ax10o 1952. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.)

Assertion

Ref	Expression
ax-10o	⊢ (∀x x = y → (∀xφ → ∀yφ))

Detailed syntax breakdown of Axiom ax-10o

Step	Hyp	Ref	Expression
1		vx	. . . 4 setvar x
2		vy	. . . 4 setvar y
3	1, 2	weq 1643	. . 3 wff x = y
4	3, 1	wal 1540	. 2 wff ∀x x = y
5		wph	. . . 4 wff φ
6	5, 1	wal 1540	. . 3 wff ∀xφ
7	5, 2	wal 1540	. . 3 wff ∀yφ
8	6, 7	wi 4	. 2 wff (∀xφ → ∀yφ)
9	4, 8	wi 4	1 wff (∀x x = y → (∀xφ → ∀yφ))

This axiom is referenced by:  aecom-o  2151  hbae-o  2153  dral1-o  2154  ax10from10o  2177  dvelimf-o  2180