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Theorem aev 1991
 Description: A "distinctor elimination" lemma with no restrictions on variables in the consequent. (Contributed by NM, 8-Nov-2006.)
Assertion
Ref Expression
aev (x x = yz w = v)
Distinct variable group:   x,y

Proof of Theorem aev
Dummy variable u is distinct from all other variables.
StepHypRef Expression
1 hbae 1953 . 2 (x x = yzx x = y)
2 ax10lem5 1942 . . 3 (x x = yu u = v)
3 ax-8 1675 . . . 4 (u = w → (u = vw = v))
43spimv 1990 . . 3 (u u = vw = v)
52, 4syl 15 . 2 (x x = yw = v)
61, 5alrimih 1565 1 (x x = yz w = v)
 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:  ax16ALT2  2048  a16gALT  2049
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