Theorem preq2i 4673

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 4670	. 2 ⊢ (𝐴 = 𝐵 → {𝐶, 𝐴} = {𝐶, 𝐵})
3	1, 2	ax-mp 5	1 ⊢ {𝐶, 𝐴} = {𝐶, 𝐵}

Syntax hints:   = wceq 1539  {cpr 4563

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-un 3892  df-sn 4562  df-pr 4564

This theorem is referenced by:  opidg  4823  funopg  6468  df2o2  8306  fz12pr  13313  fz0to3un2pr  13358  fz0to4untppr  13359  fzo13pr  13471  fzo0to2pr  13472  fzo0to42pr  13474  bpoly3  15768  prmreclem2  16618  2strstr1OLD  16938  mgmnsgrpex  18570  sgrpnmndex  18571  m2detleiblem2  21777  txindis  22785  setsvtx  27405  uhgrwkspthlem2  28122  31prm  45049  nnsum3primes4  45240  nnsum3primesgbe  45244