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Theorem ax10from10o 2177
 Description: Rederivation of ax-10 2140 from original version ax-10o 2139. See theorem ax10o 1952 for the derivation of ax-10o 2139 from ax-10 2140. This theorem should not be referenced in any proof. Instead, use ax-10 2140 above so that uses of ax-10 2140 can be more easily identified, or use aecom-o 2151 when this form is needed for studies involving ax-10o 2139 and omitting ax-17 1616. (Contributed by NM, 16-May-2008.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax10from10o (x x = yy y = x)

Proof of Theorem ax10from10o
StepHypRef Expression
1 ax-10o 2139 . . 3 (x x = y → (x x = yy x = y))
21pm2.43i 43 . 2 (x x = yy x = y)
3 equcomi 1679 . . 3 (x = yy = x)
43alimi 1559 . 2 (y x = yy y = x)
52, 4syl 15 1 (x x = yy y = x)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-10o 2139 This theorem depends on definitions:  df-bi 177  df-ex 1542 This theorem is referenced by: (None)
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