Theorem preq2i 4742

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

Step	Hyp	Ref	Expression
1		preq1i.1	. 2 ⊢ 𝐴 = 𝐵
2		preq2 4739	. 2 ⊢ (𝐴 = 𝐵 → {𝐶, 𝐴} = {𝐶, 𝐵})
3	1, 2	ax-mp 5	1 ⊢ {𝐶, 𝐴} = {𝐶, 𝐵}

Syntax hints:   = wceq 1537  {cpr 4633

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-un 3968  df-sn 4632  df-pr 4634

This theorem is referenced by:  opidg  4897  funopg  6602  df2o2  8514  fz12pr  13618  fz0to3un2pr  13666  fz0to4untppr  13667  fzo13pr  13785  fzo0to2pr  13786  fz01pr  13787  fzo0to42pr  13789  bpoly3  16091  prmreclem2  16951  2strstr1OLD  17271  mgmnsgrpex  18957  sgrpnmndex  18958  m2detleiblem2  22650  txindis  23658  setsvtx  29067  uhgrwkspthlem2  29787  31prm  47522  nnsum3primes4  47713  nnsum3primesgbe  47717