Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > infeq123d | Unicode version |
Description: Equality deduction for infimum. (Contributed by AV, 2-Sep-2020.) |
Ref | Expression |
---|---|
infeq123d.a | |
infeq123d.b | |
infeq123d.c |
Ref | Expression |
---|---|
infeq123d | inf inf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | infeq123d.a | . . 3 | |
2 | infeq123d.b | . . 3 | |
3 | infeq123d.c | . . . 4 | |
4 | 3 | cnveqd 4685 | . . 3 |
5 | 1, 2, 4 | supeq123d 6846 | . 2 |
6 | df-inf 6840 | . 2 inf | |
7 | df-inf 6840 | . 2 inf | |
8 | 5, 6, 7 | 3eqtr4g 2175 | 1 inf inf |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 ccnv 4508 csup 6837 infcinf 6838 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-rab 2402 df-in 3047 df-ss 3054 df-uni 3707 df-br 3900 df-opab 3960 df-cnv 4517 df-sup 6839 df-inf 6840 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |