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Theorem dveeq1-o16 2188
 Description: Version of dveeq1 2018 using ax-16 2144 instead of ax-17 1616. (Contributed by NM, 29-Apr-2008.) TO DO: Recover proof from older set.mm to remove use of ax-17 1616. (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dveeq1-o16 x x = y → (y = zx y = z))
Distinct variable group:   x,z

Proof of Theorem dveeq1-o16
Dummy variable w is distinct from all other variables.
StepHypRef Expression
1 ax17eq 2183 . 2 (w = zx w = z)
2 ax17eq 2183 . 2 (y = zw y = z)
3 equequ1 1684 . 2 (w = y → (w = zy = z))
41, 2, 3dvelimh 1964 1 x x = y → (y = zx y = z))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → 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-7 1734  ax-11 1746  ax-12 1925  ax-12o 2142  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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