Theorem preq2i 4705

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 4702	. 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 4593

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 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-un 3911  df-sn 4592  df-pr 4594

This theorem is used by:  opidg  4859  funopg  6574  df2o2  8468  fz12pr  13626  fz0to3un2pr  13674  fz0to4untppr  13675  fzo13pr  13795  fzo0to2pr  13796  fz01pr  13797  fzo0to42pr  13799  bpoly3  16134  prmreclem2  16999  mgmnsgrpex  19030  sgrpnmndex  19031  m2detleiblem2  22835  txindis  23842  setsvtx  29440  uhgrwkspthlem2  30167  31prm  48407  nnsum3primes4  48611  nnsum3primesgbe  48615  gpg5edgnedg  48953