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Theorem infeq1i 6614
Description: Equality inference for infimum. (Contributed by AV, 2-Sep-2020.)
Hypothesis
Ref Expression
infeq1i.1  |-  B  =  C
Assertion
Ref Expression
infeq1i  |- inf ( B ,  A ,  R
)  = inf ( C ,  A ,  R
)

Proof of Theorem infeq1i
StepHypRef Expression
1 infeq1i.1 . 2  |-  B  =  C
2 infeq1 6612 . 2  |-  ( B  =  C  -> inf ( B ,  A ,  R
)  = inf ( C ,  A ,  R
) )
31, 2ax-mp 7 1  |- inf ( B ,  A ,  R
)  = inf ( C ,  A ,  R
)
Colors of variables: wff set class
Syntax hints:    = wceq 1285  infcinf 6584
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-rab 2362  df-uni 3628  df-sup 6585  df-inf 6586
This theorem is referenced by:  mincom  10484  lcmcom  10825  lcmass  10846
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