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Axiom ax-11o 1940
 Description: Axiom ax-11o 1940 ("o" for "old") was the original version of ax-11 1624, before it was discovered (in Jan. 2007) that the shorter ax-11 1624 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 1939. Normally, ax11o 1939 should be used rather than ax-11o 1940, except by theorems specifically studying the latter's properties. (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 1620 . . . 4
43, 1wal 1532 . . 3
54wn 5 . 2
6 wph . . . 4
73, 6wi 6 . . . . 5
87, 1wal 1532 . . . 4
96, 8wi 6 . . 3
103, 9wi 6 . 2
115, 10wi 6 1
 Colors of variables: wff set class This axiom is referenced by:  ax11  1941  ax11b  1942  a12study  27821  a12studyALT  27822  a12study3  27824
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