Theorem preq2i 4700

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 4697	. 2 ⊢ (𝐴 = 𝐵 → {𝐶, 𝐴} = {𝐶, 𝐵})
3	1, 2	ax-mp 5	1 ⊢ {𝐶, 𝐴} = {𝐶, 𝐵}

This proof depends on syntax axioms:   = wceq 1570  {cpr 4590

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-un 4154  df-sn 4589  df-pr 4591

This theorem is used by:  opidg  4857  funopg  6602  df2o2  8523  fz12pr  13755  fz0to3un2pr  13803  fz0to4untppr  13804  fzo13pr  13924  fzo0to2pr  13925  fz01pr  13926  fzo0to42pr  13928  bpoly3  16268  mgmnsgrpex  19180  sgrpnmndex  19181  m2detleiblem2  22998  txindis  24008  setsvtx  29670  31prm  48955  nnsum3primes4  49159  nnsum3primesgbe  49163  gpg5edgnedg  49501