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Axiom ax-i9 1439
Description: Axiom of Existence. One of the equality and substitution axioms of predicate calculus with equality. One thing this axiom tells us is that at least one thing exists (although ax-4 1416 and possibly others also tell us that, i.e. they are not valid in the empty domain of a "free logic"). In this form (not requiring that  x and  y be distinct) it was used in an axiom system of Tarski (see Axiom B7' in footnote 1 of [KalishMontague] p. 81.) Another name for this theorem is a9e 1602, which has additional remarks. (Contributed by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
ax-i9  |-  E. x  x  =  y

Detailed syntax breakdown of Axiom ax-i9
StepHypRef Expression
1 vx . . 3  setvar  x
2 vy . . 3  setvar  y
31, 2weq 1408 . 2  wff  x  =  y
43, 1wex 1397 1  wff  E. x  x  =  y
Colors of variables: wff set class
This axiom is referenced by:  ax-9  1440  a9e  1602  a9ev  1603  sbcof2  1707
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