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Mirrors > Home > ILE Home > Th. List > rexdifpr | Unicode version |
Description: Restricted existential quantification over a set with two elements removed. (Contributed by Alexander van der Vekens, 7-Feb-2018.) |
Ref | Expression |
---|---|
rexdifpr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldifpr 3610 | . . . . 5 | |
2 | 3anass 977 | . . . . 5 | |
3 | 1, 2 | bitri 183 | . . . 4 |
4 | 3 | anbi1i 455 | . . 3 |
5 | anass 399 | . . . 4 | |
6 | df-3an 975 | . . . . . 6 | |
7 | 6 | bicomi 131 | . . . . 5 |
8 | 7 | anbi2i 454 | . . . 4 |
9 | 5, 8 | bitri 183 | . . 3 |
10 | 4, 9 | bitri 183 | . 2 |
11 | 10 | rexbii2 2481 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 w3a 973 wcel 2141 wne 2340 wrex 2449 cdif 3118 cpr 3584 |
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-in1 609 ax-in2 610 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 |
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-ne 2341 df-rex 2454 df-v 2732 df-dif 3123 df-un 3125 df-sn 3589 df-pr 3590 |
This theorem is referenced by: (None) |
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