Axiom ax-10o 1177

Description: Axiom ax-10o 1177 ("o" for "old") was the original version of ax-10 1002, before it was discovered (in May 2008) that the shorter ax-10 1002 could replace it. It appears as Axiom scheme C11' in [Megill] p. 448 (p. 16 of the preprint).

This axiom is redundant, as shown by theorem ax10o 1176.

Assertion

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

Detailed syntax breakdown of Axiom ax-10o

Step	Hyp	Ref	Expression
1		vx	. . . . 5 set x
2	1	cv 991	. . . 4 class x
3		vy	. . . . 5 set y
4	3	cv 991	. . . 4 class y
5	2, 4	wceq 992	. . 3 wff x = y
6	5, 1	wal 990	. 2 wff ∀x x = y
7		wph	. . . 4 wff φ
8	7, 1	wal 990	. . 3 wff ∀xφ
9	7, 3	wal 990	. . 3 wff ∀yφ
10	8, 9	wi 3	. 2 wff (∀xφ → ∀yφ)
11	6, 10	wi 3	1 wff (∀x x = y → (∀xφ → ∀yφ))

This axiom is referenced by:  ax10 1178  hbae 1182  dvelimfALT 1190  dral1 1191  hbsb4 1286  a12stdy1 1411  a12stdy2 1412  a12stdy4 1414  hbeu 1428  nd1 5092  nd2 5093  axpowndlem3 5105

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