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Axiom ax-i9 1464
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 1441 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 1627, which has additional remarks. (Contributed by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
ax-i9 𝑥 𝑥 = 𝑦

Detailed syntax breakdown of Axiom ax-i9
StepHypRef Expression
1 vx . . 3 setvar 𝑥
2 vy . . 3 setvar 𝑦
31, 2weq 1433 . 2 wff 𝑥 = 𝑦
43, 1wex 1422 1 wff 𝑥 𝑥 = 𝑦
Colors of variables: wff set class
This axiom is referenced by:  ax-9  1465  a9e  1627  a9ev  1628  sbcof2  1733
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