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Theorem ax10 1678
Description: Rederivation of ax-10 1466 from original version ax-10o 1677. See theorem ax10o 1676 for the derivation of ax-10o 1677 from ax-10 1466.

This theorem should not be referenced in any proof. Instead, use ax-10 1466 above so that uses of ax-10 1466 can be more easily identified. (Contributed by NM, 16-May-2008.) (New usage is discouraged.)

Assertion
Ref Expression
ax10  |-  ( A. x  x  =  y  ->  A. y  y  =  x )

Proof of Theorem ax10
StepHypRef Expression
1 ax-10o 1677 . . 3  |-  ( A. x  x  =  y  ->  ( A. x  x  =  y  ->  A. y  x  =  y )
)
21pm2.43i 49 . 2  |-  ( A. x  x  =  y  ->  A. y  x  =  y )
3 equcomi 1663 . . 3  |-  ( x  =  y  ->  y  =  x )
43alimi 1414 . 2  |-  ( A. y  x  =  y  ->  A. y  y  =  x )
52, 4syl 14 1  |-  ( A. x  x  =  y  ->  A. y  y  =  x )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1312
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-5 1406  ax-gen 1408  ax-ie2 1453  ax-8 1465  ax-17 1489  ax-i9 1493  ax-10o 1677
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
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