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Theorem equidOLD 1692
Description: Obsolete proof of equid 1691 as of 9-Dec-2017. (Contributed by NM, 1-Apr-2005.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
equidOLD  |-  x  =  x

Proof of Theorem equidOLD
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 ax9v 1670 . . 3  |-  -.  A. y  -.  y  =  x
2 ax-8 1690 . . . . . 6  |-  ( y  =  x  ->  (
y  =  x  ->  x  =  x )
)
32pm2.43i 46 . . . . 5  |-  ( y  =  x  ->  x  =  x )
43con3i 130 . . . 4  |-  ( -.  x  =  x  ->  -.  y  =  x
)
54alimi 1569 . . 3  |-  ( A. y  -.  x  =  x  ->  A. y  -.  y  =  x )
61, 5mto 170 . 2  |-  -.  A. y  -.  x  =  x
7 ax-17 1628 . 2  |-  ( -.  x  =  x  ->  A. y  -.  x  =  x )
86, 7mt3 174 1  |-  x  =  x
Colors of variables: wff set class
Syntax hints:   -. wn 3   A.wal 1550
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690
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