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Theorem equid1 1820
Description: Identity law for equality (reflexivity). Lemma 6 of [Tarski] p. 68. This proof is similar to Tarski's and makes use of a dummy variable  y. See equid 1818 for a proof that avoids dummy variables (but is less intuitive). (Contributed by NM, 1-Apr-2005.) (Proof modification is discouraged.)
Assertion
Ref Expression
equid1  |-  x  =  x

Proof of Theorem equid1
StepHypRef Expression
1 a9e 1817 . 2  |-  E. y 
y  =  x
2 ax-17 1628 . . 3  |-  ( x  =  x  ->  A. y  x  =  x )
3 ax-8 1623 . . . 4  |-  ( y  =  x  ->  (
y  =  x  ->  x  =  x )
)
43pm2.43i 45 . . 3  |-  ( y  =  x  ->  x  =  x )
52, 4exlimih 1782 . 2  |-  ( E. y  y  =  x  ->  x  =  x )
61, 5ax-mp 10 1  |-  x  =  x
Colors of variables: wff set class
Syntax hints:   E.wex 1537
This theorem is referenced by:  equcomi  1822  ax16i  1994
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-8 1623  ax-17 1628  ax-9 1684  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540
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