Theorem preq1i 3698

Description: Equality inference for unordered pairs. (Contributed by NM, 19-Oct-2012.)

Hypothesis

Ref	Expression
preq1i.1	|- A = B

Assertion

Ref	Expression
preq1i	|- { A , C } = { B , C }

Proof of Theorem preq1i

Step	Hyp	Ref	Expression
1		preq1i.1	. 2 |- A = B
2		preq1 3695	. 2 |- ( A = B -> { A , C } = { B , C } )
3	1, 2	ax-mp 5	1 |- { A , C } = { B , C }

Syntax hints:   = wceq 1364   {cpr 3619

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-un 3157  df-sn 3624  df-pr 3625

This theorem is referenced by:  funopg  5280