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Theorem ax10lem3 1938
 Description: Lemma for ax10 1944. Similar to ax-10 2140 but with distinct variables. (Contributed by NM, 25-Jul-2015.)
Assertion
Ref Expression
ax10lem3 (x x = yy y = x)
Distinct variable group:   x,y

Proof of Theorem ax10lem3
Dummy variables w z are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ax10lem2 1937 . 2 (x x = yx x = z)
2 ax10lem1 1936 . . . 4 (x x = zw w = z)
3 ax10lem2 1937 . . . 4 (w w = zw w = x)
42, 3syl 15 . . 3 (x x = zw w = x)
5 ax10lem1 1936 . . 3 (w w = xy y = x)
64, 5syl 15 . 2 (x x = zy y = x)
71, 6syl 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-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545 This theorem is referenced by:  dvelimv  1939
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