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Mirrors > Home > ILE Home > Th. List > joinlmuladdmuld | Unicode version |
Description: Join AB+CB into (A+C) on LHS. (Contributed by David A. Wheeler, 26-Oct-2019.) |
Ref | Expression |
---|---|
joinlmuladdmuld.1 | |
joinlmuladdmuld.2 | |
joinlmuladdmuld.3 | |
joinlmuladdmuld.4 |
Ref | Expression |
---|---|
joinlmuladdmuld |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | joinlmuladdmuld.1 | . . 3 | |
2 | joinlmuladdmuld.3 | . . 3 | |
3 | joinlmuladdmuld.2 | . . 3 | |
4 | 1, 2, 3 | adddird 7934 | . 2 |
5 | joinlmuladdmuld.4 | . 2 | |
6 | 4, 5 | eqtrd 2203 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wcel 2141 (class class class)co 5851 cc 7761 caddc 7766 cmul 7768 |
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 7859 ax-mulcom 7864 ax-distr 7867 |
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 5854 |
This theorem is referenced by: div4p1lem1div2 9120 arisum 11450 tangtx 13514 binom4 13652 |
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