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 1542  {cpr 4631

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 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-un 3954  df-sn 4630  df-pr 4632

This theorem is referenced by:  opidg  4893  funopg  6583  df2o2  8475  fz12pr  13558  fz0to3un2pr  13603  fz0to4untppr  13604  fzo13pr  13716  fzo0to2pr  13717  fzo0to42pr  13719  bpoly3  16002  prmreclem2  16850  2strstr1OLD  17170  mgmnsgrpex  18812  sgrpnmndex  18813  m2detleiblem2  22130  txindis  23138  setsvtx  28295  uhgrwkspthlem2  29011  31prm  46265  nnsum3primes4  46456  nnsum3primesgbe  46460