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Theorem axc11nfromc11 2249
Description: Rederivation of ax-c11n 2212 from original version ax-c11 2211. See theorem axc11 2027 for the derivation of ax-c11 2211 from ax-c11n 2212.

This theorem should not be referenced in any proof. Instead, use ax-c11n 2212 above so that uses of ax-c11n 2212 can be more easily identified, or use aecom-o 2223 when this form is needed for studies involving ax-c11 2211 and omitting ax-5 1680. (Contributed by NM, 16-May-2008.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion
Ref Expression
axc11nfromc11  |-  ( A. x  x  =  y  ->  A. y  y  =  x )

Proof of Theorem axc11nfromc11
StepHypRef Expression
1 ax-c11 2211 . . 3  |-  ( A. x  x  =  y  ->  ( A. x  x  =  y  ->  A. y  x  =  y )
)
21pm2.43i 47 . 2  |-  ( A. x  x  =  y  ->  A. y  x  =  y )
3 equcomi 1742 . . 3  |-  ( x  =  y  ->  y  =  x )
43alimi 1614 . 2  |-  ( A. y  x  =  y  ->  A. y  y  =  x )
52, 4syl 16 1  |-  ( A. x  x  =  y  ->  A. y  y  =  x )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1377
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-c11 2211
This theorem depends on definitions:  df-bi 185  df-ex 1597
This theorem is referenced by: (None)
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