Theorem preq2i 4685

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 4682	. 2 ⊢ (𝐴 = 𝐵 → {𝐶, 𝐴} = {𝐶, 𝐵})
3	1, 2	ax-mp 5	1 ⊢ {𝐶, 𝐴} = {𝐶, 𝐵}

Syntax hints:   = wceq 1541  {cpr 4573

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-v 3438  df-un 3902  df-sn 4572  df-pr 4574

This theorem is referenced by:  opidg  4839  funopg  6510  df2o2  8389  fz12pr  13476  fz0to3un2pr  13524  fz0to4untppr  13525  fzo13pr  13644  fzo0to2pr  13645  fz01pr  13646  fzo0to42pr  13648  bpoly3  15960  prmreclem2  16824  mgmnsgrpex  18834  sgrpnmndex  18835  m2detleiblem2  22538  txindis  23544  setsvtx  29008  uhgrwkspthlem2  29727  31prm  47628  nnsum3primes4  47819  nnsum3primesgbe  47823  gpg5edgnedg  48161