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Theorem equid1 1267
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 1124 for a proof that avoids dummy variables (but is less intuitive).
Assertion
Ref Expression
equid1 |- x = x
Proof of Theorem equid1
StepHypRef Expression
1 a9e 1123 . 2 |- E.y y = x
2 ax-17 969 . . 3 |- (x = x -> A.y x = x)
3 ax-8 962 . . . 4 |- (y = x -> (y = x -> x = x))
43pm2.43i 64 . . 3 |- (y = x -> x = x)
52, 419.23ai 1062 . 2 |- (E.y y = x -> x = x)
61, 5ax-mp 7 1 |- x = x
Colors of variables: wff set class
Syntax hints:   = wceq 954  E.wex 978
This theorem is referenced by:  ax16i 1268  a12study 1376
This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-8 962  ax-9 963  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976
This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 979
Copyright terms: Public domain