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Theorem uneq2 3275
Description: Equality theorem for the union of two classes. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
uneq2  |-  ( A  =  B  ->  ( C  u.  A )  =  ( C  u.  B ) )

Proof of Theorem uneq2
StepHypRef Expression
1 uneq1 3274 . 2  |-  ( A  =  B  ->  ( A  u.  C )  =  ( B  u.  C ) )
2 uncom 3271 . 2  |-  ( C  u.  A )  =  ( A  u.  C
)
3 uncom 3271 . 2  |-  ( C  u.  B )  =  ( B  u.  C
)
41, 2, 33eqtr4g 2228 1  |-  ( A  =  B  ->  ( C  u.  A )  =  ( C  u.  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1348    u. cun 3119
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125
This theorem is referenced by:  uneq12  3276  uneq2i  3278  uneq2d  3281  uneqin  3378  disjssun  3477  uniprg  3809  sucprc  4395  unexb  4425  unfiexmid  6892  unfidisj  6896  hashunlem  10728  bdunexb  13917  bj-unexg  13918
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