![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > addcanad | Unicode version |
Description: Cancelling a term on the left-hand side of a sum in an equality. Consequence of addcand 8140. (Contributed by David Moews, 28-Feb-2017.) |
Ref | Expression |
---|---|
addcand.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
addcand.2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
addcand.3 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
addcanad.4 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
addcanad |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addcanad.4 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | addcand.1 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | addcand.2 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | addcand.3 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 2, 3, 4 | addcand 8140 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | 1, 5 | mpbid 147 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-resscn 7902 ax-1cn 7903 ax-icn 7905 ax-addcl 7906 ax-addrcl 7907 ax-mulcl 7908 ax-addcom 7910 ax-addass 7912 ax-distr 7914 ax-i2m1 7915 ax-0id 7918 ax-rnegex 7919 ax-cnre 7921 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4004 df-iota 5178 df-fv 5224 df-ov 5877 |
This theorem is referenced by: divalglemqt 11923 |
Copyright terms: Public domain | W3C validator |