Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ctiunctlemu1st | Unicode version |
Description: Lemma for ctiunct 11953. (Contributed by Jim Kingdon, 28-Oct-2023.) |
Ref | Expression |
---|---|
ctiunct.som | |
ctiunct.sdc | DECID |
ctiunct.f | |
ctiunct.tom | |
ctiunct.tdc | DECID |
ctiunct.g | |
ctiunct.j | |
ctiunct.u | |
ctiunctlem.n |
Ref | Expression |
---|---|
ctiunctlemu1st |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ctiunctlem.n | . . . 4 | |
2 | 2fveq3 5426 | . . . . . . 7 | |
3 | 2 | eleq1d 2208 | . . . . . 6 |
4 | 2fveq3 5426 | . . . . . . 7 | |
5 | 2 | fveq2d 5425 | . . . . . . . 8 |
6 | 5 | csbeq1d 3010 | . . . . . . 7 |
7 | 4, 6 | eleq12d 2210 | . . . . . 6 |
8 | 3, 7 | anbi12d 464 | . . . . 5 |
9 | ctiunct.u | . . . . 5 | |
10 | 8, 9 | elrab2 2843 | . . . 4 |
11 | 1, 10 | sylib 121 | . . 3 |
12 | 11 | simprd 113 | . 2 |
13 | 12 | simpld 111 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 DECID wdc 819 wceq 1331 wcel 1480 wral 2416 crab 2420 csb 3003 wss 3071 com 4504 cxp 4537 wfo 5121 wf1o 5122 cfv 5123 c1st 6036 c2nd 6037 |
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 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-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-rab 2425 df-v 2688 df-sbc 2910 df-csb 3004 df-un 3075 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-iota 5088 df-fv 5131 |
This theorem is referenced by: ctiunctlemf 11951 |
Copyright terms: Public domain | W3C validator |