Axiom ax-10o 1781

Description: Axiom ax-10o 1781 ("o" for "old") was the original version of ax-10 1596, before it was discovered (in May 2008) that the shorter ax-10 1596 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 1780.

Assertion

Ref	Expression
ax-10o	|- (A.x x = y -> (A.xph -> A.yph))

Detailed syntax breakdown of Axiom ax-10o

Step	Hyp	Ref	Expression
1		vx	. . . . 5 set x
2	1	cv 1585	. . . 4 class x
3		vy	. . . . 5 set y
4	3	cv 1585	. . . 4 class y
5	2, 4	wceq 1586	. . 3 wff x = y
6	5, 1	wal 1584	. 2 wff A.x x = y
7		wph	. . . 4 wff ph
8	7, 1	wal 1584	. . 3 wff A.xph
9	7, 3	wal 1584	. . 3 wff A.yph
10	8, 9	wi 3	. 2 wff (A.xph -> A.yph)
11	6, 10	wi 3	1 wff (A.x x = y -> (A.xph -> A.yph))

This axiom is referenced by:  ax10 1782  hbae 1786  dvelimfALT 1794  dral1 1795  hbsb4 1895  a12stdy1 2027  a12stdy2 2028  a12stdy4 2030  hbeu 2048  hbeud 2049  nd1 6457  nd2 6458  axpowndlem3 6469

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