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Mirrors > Home > ILE Home > Th. List > infeq3 | Unicode version |
Description: Equality theorem for infimum. (Contributed by AV, 2-Sep-2020.) |
Ref | Expression |
---|---|
infeq3 | inf inf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnveq 4783 | . . 3 | |
2 | supeq3 6963 | . . 3 | |
3 | 1, 2 | syl 14 | . 2 |
4 | df-inf 6958 | . 2 inf | |
5 | df-inf 6958 | . 2 inf | |
6 | 3, 4, 5 | 3eqtr4g 2228 | 1 inf inf |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 ccnv 4608 csup 6955 infcinf 6956 |
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 609 ax-in2 610 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-ral 2453 df-rex 2454 df-rab 2457 df-in 3127 df-ss 3134 df-uni 3795 df-br 3988 df-opab 4049 df-cnv 4617 df-sup 6957 df-inf 6958 |
This theorem is referenced by: (None) |
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