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Theorem equid1ALT 2253
Description: Identity law for equality (reflexivity). Lemma 6 of [Tarski] p. 68. Alternate proof of equid1 2235 from older axioms ax-6o 2214 and ax-9o 2215. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
equid1ALT  |-  x  =  x

Proof of Theorem equid1ALT
StepHypRef Expression
1 ax-12o 2219 . . . . 5  |-  ( -. 
A. x  x  =  x  ->  ( -.  A. x  x  =  x  ->  ( x  =  x  ->  A. x  x  =  x )
) )
21pm2.43i 45 . . . 4  |-  ( -. 
A. x  x  =  x  ->  ( x  =  x  ->  A. x  x  =  x )
)
32alimi 1568 . . 3  |-  ( A. x  -.  A. x  x  =  x  ->  A. x
( x  =  x  ->  A. x  x  =  x ) )
4 ax-9o 2215 . . 3  |-  ( A. x ( x  =  x  ->  A. x  x  =  x )  ->  x  =  x )
53, 4syl 16 . 2  |-  ( A. x  -.  A. x  x  =  x  ->  x  =  x )
6 ax-6o 2214 . 2  |-  ( -. 
A. x  -.  A. x  x  =  x  ->  x  =  x )
75, 6pm2.61i 158 1  |-  x  =  x
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1549
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-6o 2214  ax-9o 2215  ax-12o 2219
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