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Axiom ax-11o 1590
Description: Axiom ax-11o 1590 ("o" for "old") was the original version of ax-11 1330, before it was discovered (in Jan. 2007) that the shorter ax-11 1330 could replace it. It appears as Axiom scheme C15' in [Megill] p. 448 (p. 16 of the preprint). It is based on Lemma 16 of [Tarski] p. 70 and Axiom C8 of [Monk2] p. 105, from which it can be proved by cases. To understand this theorem more easily, think of " ..." as informally meaning "if and are distinct variables then..." The antecedent becomes false if the same variable is substituted for and , ensuring the theorem is sound whenever this is the case. In some later theorems, we call an antecedent of the form a "distinctor."

This axiom is redundant, as shown by theorem ax11o 1589.

This axiom is obsolete and should no longer be used. It is proved above as theorem ax11o 1589. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.)

Assertion
Ref Expression
ax-11o

Detailed syntax breakdown of Axiom ax-11o
StepHypRef Expression
1 vx . . . . 5
2 vy . . . . 5
31, 2weq 1325 . . . 4
43, 1wal 1266 . . 3
54wn 3 . 2
6 wph . . . 4
73, 6wi 4 . . . . 5
87, 1wal 1266 . . . 4
96, 8wi 4 . . 3
103, 9wi 4 . 2
115, 10wi 4 1
Colors of variables: wff set class
This axiom is referenced by:  ax11b  1593
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