This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem entr3i

Description: A chained equinumerosity inference. (Contributed by NM, 25-Sep-2004)

Ref Expression
Hypotheses entr3i.1 ⊢ A ≈ B
entr3i.2 ⊢ A ≈ C
Assertion entr3i ⊢ B ≈ C

Proof

Step Hyp Ref Expression
1 entr3i.1 ⊢ A ≈ B
2 entr3i.2 ⊢ A ≈ C
3 1 ensymi ⊢ B ≈ A
4 3 2 entri ⊢ B ≈ C