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Axiom ax-10 1412
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 1620 ("o" for "old") and was replaced with this shorter ax-10 1412 in May 2008. The old axiom is proved from this one as theorem ax10o 1619. Conversely, this axiom is proved from ax-10o 1620 as theorem ax10 1621. (Contributed by NM, 5-Aug-1993.)

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

Detailed syntax breakdown of Axiom ax-10
StepHypRef Expression
1 vx . . . 4  setvar  x
2 vy . . . 4  setvar  y
31, 2weq 1408 . . 3  wff  x  =  y
43, 1wal 1257 . 2  wff  A. x  x  =  y
52, 1weq 1408 . . 3  wff  y  =  x
65, 2wal 1257 . 2  wff  A. y 
y  =  x
74, 6wi 4 1  wff  ( A. x  x  =  y  ->  A. y  y  =  x )
Colors of variables: wff set class
This axiom is referenced by:  alequcom  1424  ax10o  1619  naecoms  1628  oprabidlem  5563
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