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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 |
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joinlmuladdmuld.2 |
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joinlmuladdmuld.3 |
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joinlmuladdmuld.4 |
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Ref | Expression |
---|---|
joinlmuladdmuld |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | joinlmuladdmuld.1 |
. . 3
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2 | joinlmuladdmuld.3 |
. . 3
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3 | joinlmuladdmuld.2 |
. . 3
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4 | 1, 2, 3 | adddird 7610 |
. 2
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5 | joinlmuladdmuld.4 |
. 2
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6 | 4, 5 | eqtrd 2127 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-addcl 7538 ax-mulcom 7543 ax-distr 7546 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-nf 1402 df-sb 1700 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-rex 2376 df-v 2635 df-un 3017 df-sn 3472 df-pr 3473 df-op 3475 df-uni 3676 df-br 3868 df-iota 5014 df-fv 5057 df-ov 5693 |
This theorem is referenced by: div4p1lem1div2 8767 arisum 11056 |
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