Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > add4 | Unicode version |
Description: Rearrangement of 4 terms in a sum. (Contributed by NM, 13-Nov-1999.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
Ref | Expression |
---|---|
add4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | add12 8064 | . . . . 5 | |
2 | 1 | 3expb 1199 | . . . 4 |
3 | 2 | oveq2d 5866 | . . 3 |
4 | 3 | adantll 473 | . 2 |
5 | addcl 7886 | . . 3 | |
6 | addass 7891 | . . . 4 | |
7 | 6 | 3expa 1198 | . . 3 |
8 | 5, 7 | sylan2 284 | . 2 |
9 | addcl 7886 | . . . 4 | |
10 | addass 7891 | . . . . 5 | |
11 | 10 | 3expa 1198 | . . . 4 |
12 | 9, 11 | sylan2 284 | . . 3 |
13 | 12 | an4s 583 | . 2 |
14 | 4, 8, 13 | 3eqtr4d 2213 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wcel 2141 (class class class)co 5850 cc 7759 caddc 7764 |
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 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 ax-addcl 7857 ax-addcom 7861 ax-addass 7863 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rex 2454 df-v 2732 df-un 3125 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-iota 5158 df-fv 5204 df-ov 5853 |
This theorem is referenced by: add42 8068 add4i 8071 add4d 8075 3dvds2dec 11812 opoe 11841 ptolemy 13460 |
Copyright terms: Public domain | W3C validator |