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Theorem preq2i 4703
Description: Equality inference for unordered pairs. (Contributed by NM, 19-Oct-2012.)
Hypothesis
Ref Expression
preq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
preq2i {𝐶, 𝐴} = {𝐶, 𝐵}

Proof of Theorem preq2i
StepHypRef Expression
1 preq1i.1 . 2 𝐴 = 𝐵
2 preq2 4700 . 2 (𝐴 = 𝐵 → {𝐶, 𝐴} = {𝐶, 𝐵})
31, 2ax-mp 5 1 {𝐶, 𝐴} = {𝐶, 𝐵}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  {cpr 4593
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-v 3450  df-un 3920  df-sn 4592  df-pr 4594
This theorem is referenced by:  opidg  4854  funopg  6540  df2o2  8426  fz12pr  13505  fz0to3un2pr  13550  fz0to4untppr  13551  fzo13pr  13663  fzo0to2pr  13664  fzo0to42pr  13666  bpoly3  15948  prmreclem2  16796  2strstr1OLD  17116  mgmnsgrpex  18748  sgrpnmndex  18749  m2detleiblem2  21993  txindis  23001  setsvtx  28028  uhgrwkspthlem2  28744  31prm  45863  nnsum3primes4  46054  nnsum3primesgbe  46058
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