Axiom ax-10 1308

Description: Axiom of Quantifier Substitution. One of the equality and substitution axioms of predicate calculus with equality. Appears as Lemma L12 in [Megill] p. 445 (p. 12 of the preprint).

The original version of this axiom was ax-10o 1500 ("o" for "old") and was replaced with this shorter ax-10 1308 in May 2008. The old axiom is proved from this one as theorem ax10o 1499. Conversely, this axiom is proved from ax-10o 1500 as theorem ax10 1501.

Assertion

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

Detailed syntax breakdown of Axiom ax-10

Step	Hyp	Ref	Expression
1		vx	. . . . 5 set x
2	1	cv 1297	. . . 4 class x
3		vy	. . . . 5 set y
4	3	cv 1297	. . . 4 class y
5	2, 4	wceq 1298	. . 3 wff x = y
6	5, 1	wal 1296	. 2 wff A.x x = y
7	4, 2	wceq 1298	. . 3 wff y = x
8	7, 3	wal 1296	. 2 wff A.y y = x
9	6, 8	wi 3	1 wff (A.x x = y -> A.y y = x)

This axiom is referenced by:  ax10o 1499  alequcom 1502

Copyright terms: Public domain