Theorem preq1i 4669

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 4666	. 2 ⊢ (𝐴 = 𝐵 → {𝐴, 𝐶} = {𝐵, 𝐶})
3	1, 2	ax-mp 5	1 ⊢ {𝐴, 𝐶} = {𝐵, 𝐶}

Syntax hints:   = wceq 1539  {cpr 4560

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-un 3888  df-sn 4559  df-pr 4561

This theorem is referenced by:  funopg  6452  frcond1  28531  n4cyclfrgr  28556  disjdifprg2  30816