Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > sbc3an | Unicode version |
Description: Distribution of class substitution over triple conjunction. (Contributed by NM, 14-Dec-2006.) (Revised by NM, 17-Aug-2018.) |
Ref | Expression |
---|---|
sbc3an |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3an 964 | . . . 4 | |
2 | 1 | sbcbii 2968 | . . 3 |
3 | sbcan 2951 | . . 3 | |
4 | sbcan 2951 | . . . 4 | |
5 | 4 | anbi1i 453 | . . 3 |
6 | 2, 3, 5 | 3bitri 205 | . 2 |
7 | df-3an 964 | . 2 | |
8 | 6, 7 | bitr4i 186 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 w3a 962 wsbc 2909 |
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-v 2688 df-sbc 2910 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |