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Theorem elequ2 1715
 Description: An identity law for the non-logical predicate. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
elequ2 (x = y → (z xz y))

Proof of Theorem elequ2
StepHypRef Expression
1 ax-14 1714 . 2 (x = y → (z xz y))
2 ax-14 1714 . . 3 (y = x → (z yz x))
32equcoms 1681 . 2 (x = y → (z yz x))
41, 3impbid 183 1 (x = y → (z xz y))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176 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 This theorem depends on definitions:  df-bi 177  df-ex 1542 This theorem is referenced by:  ax11wdemo  1723  dveel2  2020  elsb4  2104  dveel2ALT  2191  ax11el  2194  axext3  2336  axext4  2337  bm1.1  2338  ssfin  4470  ncfinlower  4483  nnadjoinlem1  4519  fv3  5341
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