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Theorem dveel2ALT 2191
 Description: Version of dveel2 2020 using ax-16 2144 instead of ax-17 1616. (Contributed by NM, 10-May-2008.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dveel2ALT x x = y → (z yx z y))
Distinct variable group:   x,z

Proof of Theorem dveel2ALT
Dummy variable w is distinct from all other variables.
StepHypRef Expression
1 ax17el 2189 . 2 (z wx z w)
2 ax17el 2189 . 2 (z yw z y)
3 elequ2 1715 . 2 (w = y → (z wz y))
41, 2, 3dvelimh 1964 1 x x = y → (z yx z y))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → 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-14 1714  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-15 2143  ax-16 2144 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: (None)
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