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Theorem infeq1i 6866
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 6864 . 2 (𝐵 = 𝐶 → inf(𝐵, 𝐴, 𝑅) = inf(𝐶, 𝐴, 𝑅))
31, 2ax-mp 5 1 inf(𝐵, 𝐴, 𝑅) = inf(𝐶, 𝐴, 𝑅)
Colors of variables: wff set class
Syntax hints:   = wceq 1314  infcinf 6836
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ral 2396  df-rex 2397  df-rab 2400  df-uni 3705  df-sup 6837  df-inf 6838
This theorem is referenced by:  mincom  10951  xrbdtri  10996  lcmcom  11652  lcmass  11673
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