Theorem preq2i 4737

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 4734	. 2 ⊢ (𝐴 = 𝐵 → {𝐶, 𝐴} = {𝐶, 𝐵})
3	1, 2	ax-mp 5	1 ⊢ {𝐶, 𝐴} = {𝐶, 𝐵}

Syntax hints:   = wceq 1540  {cpr 4628

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-un 3956  df-sn 4627  df-pr 4629

This theorem is referenced by:  opidg  4892  funopg  6600  df2o2  8515  fz12pr  13621  fz0to3un2pr  13669  fz0to4untppr  13670  fzo13pr  13788  fzo0to2pr  13789  fz01pr  13790  fzo0to42pr  13792  bpoly3  16094  prmreclem2  16955  2strstr1OLD  17271  mgmnsgrpex  18944  sgrpnmndex  18945  m2detleiblem2  22634  txindis  23642  setsvtx  29052  uhgrwkspthlem2  29774  31prm  47584  nnsum3primes4  47775  nnsum3primesgbe  47779