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Theorem ax10lem5 1942
 Description: Lemma for ax10 1944. Change free and bound variables. (Contributed by NM, 22-Jul-2015.)
Assertion
Ref Expression
ax10lem5 (z z = wy y = x)
Distinct variable group:   z,w

Proof of Theorem ax10lem5
Dummy variables v u are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ax10lem1 1936 . . . 4 (z z = wv v = w)
2 ax10lem4 1941 . . . 4 (v v = wu u = v)
31, 2syl 15 . . 3 (z z = wu u = v)
4 ax10lem1 1936 . . 3 (u u = vx x = v)
53, 4syl 15 . 2 (z z = wx x = v)
6 ax10lem4 1941 . 2 (x x = vy y = x)
75, 6syl 15 1 (z z = wy 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-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  ax10  1944  a16g  1945  aev  1991
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