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Theorem infeq123d 6903
 Description: Equality deduction for infimum. (Contributed by AV, 2-Sep-2020.)
Hypotheses
Ref Expression
infeq123d.a
infeq123d.b
infeq123d.c
Assertion
Ref Expression
infeq123d inf inf

Proof of Theorem infeq123d
StepHypRef Expression
1 infeq123d.a . . 3
2 infeq123d.b . . 3
3 infeq123d.c . . . 4
43cnveqd 4715 . . 3
51, 2, 4supeq123d 6878 . 2
6 df-inf 6872 . 2 inf
7 df-inf 6872 . 2 inf
85, 6, 73eqtr4g 2197 1 inf inf
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1331  ccnv 4538  csup 6869  infcinf 6870 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-in1 603  ax-in2 604  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-ral 2421  df-rex 2422  df-rab 2425  df-in 3077  df-ss 3084  df-uni 3737  df-br 3930  df-opab 3990  df-cnv 4547  df-sup 6871  df-inf 6872 This theorem is referenced by: (None)
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