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Theorem preqsnd 23953
 Description: Equivalence for a pair equal to a singleton, deduction form. (Contributed by Thierry Arnoux, 27-Dec-2016.)
Hypotheses
Ref Expression
preqsnd.1
preqsnd.2
preqsnd.3
Assertion
Ref Expression
preqsnd

Proof of Theorem preqsnd
StepHypRef Expression
1 preqsnd.1 . 2
2 preqsnd.2 . 2
3 preqsnd.3 . 2
4 dfsn2 3788 . . . 4
54eqeq2i 2414 . . 3
6 preq12bg 3937 . . . 4
7 oridm 501 . . . 4
86, 7syl6bb 253 . . 3
95, 8syl5bb 249 . 2
101, 2, 3, 3, 9syl22anc 1185 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wo 358   wa 359   wceq 1649   wcel 1721  cvv 2916  csn 3774  cpr 3775 This theorem is referenced by:  disjdifprg  23970 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-v 2918  df-un 3285  df-sn 3780  df-pr 3781
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