Theorem in13 3289

Description: A rearrangement of intersection. (Contributed by NM, 27-Aug-2012.)

Assertion

Ref	Expression
in13	|- ( A i^i ( B i^i C ) ) = ( C i^i ( B i^i A ) )

Proof of Theorem in13

Step	Hyp	Ref	Expression
1		in32 3288	. 2 |- ( ( B i^i C ) i^i A ) = ( ( B i^i A ) i^i C )
2		incom 3268	. 2 |- ( A i^i ( B i^i C ) ) = ( ( B i^i C ) i^i A )
3		incom 3268	. 2 |- ( C i^i ( B i^i A ) ) = ( ( B i^i A ) i^i C )
4	1, 2, 3	3eqtr4i 2170	1 |- ( A i^i ( B i^i C ) ) = ( C i^i ( B i^i A ) )

Syntax hints:   = wceq 1331   i^i cin 3070

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-in 3077

This theorem is referenced by: (None)