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Theorem ax10 1602
 Description: Rederivation of ax-10 1393 from original version ax-10o 1601. See theorem ax10o 1600 for the derivation of ax-10o 1601 from ax-10 1393. This theorem should not be referenced in any proof. Instead, use ax-10 1393 above so that uses of ax-10 1393 can be more easily identified. (Contributed by NM, 16-May-2008.) (New usage is discouraged.)
Assertion
Ref Expression
ax10 (x x = yy y = x)

Proof of Theorem ax10
StepHypRef Expression
1 ax-10o 1601 . . 3 (x x = y → (x x = yy x = y))
21pm2.43i 43 . 2 (x x = yy x = y)
3 equcomi 1589 . . 3 (x = yy = x)
43alimi 1341 . 2 (y x = yy y = x)
52, 4syl 14 1 (x x = yy y = x)
 Colors of variables: wff set class Syntax hints:   → wi 4  ∀wal 1240 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-5 1333  ax-gen 1335  ax-ie2 1380  ax-8 1392  ax-17 1416  ax-i9 1420  ax-10o 1601 This theorem depends on definitions:  df-bi 110 This theorem is referenced by: (None)
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