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Theorem ax10lem1 1936
 Description: Lemma for ax10 1944. Change bound variable. (Contributed by NM, 22-Jul-2015.)
Assertion
Ref Expression
ax10lem1 (x x = wy y = w)
Distinct variable groups:   x,w   y,w

Proof of Theorem ax10lem1
Dummy variable v is distinct from all other variables.
StepHypRef Expression
1 ax-8 1675 . . 3 (x = v → (x = wv = w))
21cbvalivw 1674 . 2 (x x = wv v = w)
3 ax-8 1675 . . 3 (v = y → (v = wy = w))
43cbvalivw 1674 . 2 (v v = wy y = w)
52, 4syl 15 1 (x x = wy y = w)
 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 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542 This theorem is referenced by:  ax10lem3  1938  ax10lem4  1941  ax10lem5  1942
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