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Mirrors > Home > ILE Home > Th. List > ineq12d | Unicode version |
Description: Equality deduction for intersection of two classes. (Contributed by NM, 24-Jun-2004.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
ineq1d.1 |
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ineq12d.2 |
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Ref | Expression |
---|---|
ineq12d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ineq1d.1 |
. 2
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2 | ineq12d.2 |
. 2
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3 | ineq12 3346 |
. 2
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4 | 1, 2, 3 | syl2anc 411 |
1
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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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-in 3150 |
This theorem is referenced by: csbing 3357 funprg 5288 funtpg 5289 offval 6118 ofrfval 6119 undifdc 6956 djudom 7126 isunitd 13481 dfrhm2 13529 isrhm 13533 rhmval 13548 2idlvalg 13842 |
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