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Theorem elequ1 1713
Description: An identity law for the non-logical predicate. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
elequ1 (x = y → (x zy z))

Proof of Theorem elequ1
StepHypRef Expression
1 ax-13 1712 . 2 (x = y → (x zy z))
2 ax-13 1712 . . 3 (y = x → (y zx z))
32equcoms 1681 . 2 (x = y → (y zx z))
41, 3impbid 183 1 (x = y → (x zy z))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176
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-13 1712
This theorem depends on definitions:  df-bi 177  df-ex 1542
This theorem is referenced by:  ax11wdemo  1723  cleljust  2014  cleljustALT  2015  dveel1  2019  ax15  2021  elsb3  2103  ax11el  2194  ncfinlower  4483  tfinnn  4534  tz6.12-2  5346
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