ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ax-10 Unicode version

Axiom ax-10 1437
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 1646 ("o" for "old") and was replaced with this shorter ax-10 1437 in May 2008. The old axiom is proved from this one as theorem ax10o 1645. Conversely, this axiom is proved from ax-10o 1646 as theorem ax10 1647. (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 1433 . . 3  wff  x  =  y
43, 1wal 1283 . 2  wff  A. x  x  =  y
52, 1weq 1433 . . 3  wff  y  =  x
65, 2wal 1283 . 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  1449  ax10o  1645  naecoms  1654  oprabidlem  5588
  Copyright terms: Public domain W3C validator