Axiom ax-10o 1142

Description: Axiom ax-10o 1142 ("o" for "old") was the original version of ax-10 968, before it was discovered (in May 2008) that the shorter ax-10 968 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 1141.

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 957	. . . 4 class x
3		vy	. . . . 5 set y
4	3	cv 957	. . . 4 class y
5	2, 4	wceq 958	. . 3 wff x = y
6	5, 1	wal 956	. 2 wff A.x x = y
7		wph	. . . 4 wff ph
8	7, 1	wal 956	. . 3 wff A.xph
9	7, 3	wal 956	. . 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 1143  hbae 1147  dvelimfALT 1155  dral1 1156  hbsb4 1250  a12stdy1 1374  a12stdy2 1375  a12stdy4 1377  hbeu 1391  nd1 4950  nd2 4951  axpowndlem3 4963

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