Theorem preq2i 4272

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 4269	. 2 |- ( A = B -> { C , A } = { C , B } )
3	1, 2	ax-mp 5	1 |- { C , A } = { C , B }

Syntax hints:   = wceq 1483   {cpr 4179

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-un 3579  df-sn 4178  df-pr 4180

This theorem is referenced by:  opid  4421  funopg  5922  df2o2  7574  fzprval  12401  fz0to3un2pr  12441  fz0to4untppr  12442  fzo13pr  12552  fzo0to2pr  12553  fzo0to42pr  12555  bpoly3  14789  prmreclem2  15621  2strstr1  15986  mgmnsgrpex  17418  sgrpnmndex  17419  m2detleiblem2  20434  txindis  21437  iblcnlem1  23554  axlowdimlem4  25825  setsvtx  25927  uhgrwkspthlem2  26650  opidORIG  34109  opidg  41297  31prm  41512  nnsum3primes4  41676  nnsum3primesgbe  41680