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Theorem uneq2i 3094
Description: Inference adding union to the left in a class equality. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
uneq1i.1  |-  A  =  B
Assertion
Ref Expression
uneq2i  |-  ( C  u.  A )  =  ( C  u.  B
)

Proof of Theorem uneq2i
StepHypRef Expression
1 uneq1i.1 . 2  |-  A  =  B
2 uneq2 3091 . 2  |-  ( A  =  B  ->  ( C  u.  A )  =  ( C  u.  B ) )
31, 2ax-mp 7 1  |-  ( C  u.  A )  =  ( C  u.  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1243    u. cun 2915
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922
This theorem is referenced by:  un4  3103  unundir  3105  difun2  3302  difdifdirss  3307  qdass  3467  qdassr  3468  unisuc  4150  iunsuc  4157  fmptap  5353  fvsnun1  5360  rdgival  5969  rdg0  5974
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