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Theorem oteq123d 3999
 Description: Equality deduction for ordered triples. (Contributed by Mario Carneiro, 11-Jan-2017.)
Hypotheses
Ref Expression
oteq1d.1
oteq123d.2
oteq123d.3
Assertion
Ref Expression
oteq123d

Proof of Theorem oteq123d
StepHypRef Expression
1 oteq1d.1 . . 3
21oteq1d 3996 . 2
3 oteq123d.2 . . 3
43oteq2d 3997 . 2
5 oteq123d.3 . . 3
65oteq3d 3998 . 2
72, 4, 63eqtrd 2472 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652  cotp 3818 This theorem is referenced by:  idaval  14213  coaval  14223  matval  27442  el2wlkonotot0  28339 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-ot 3824
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