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Mirrors > Home > ILE Home > Th. List > ifelpwung | Unicode version |
Description: Existence of a conditional class, quantitative version (closed form). (Contributed by BJ, 15-Aug-2024.) |
Ref | Expression |
---|---|
ifelpwung |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ifssun 3540 | . 2 | |
2 | unexg 4428 | . . 3 | |
3 | elpw2g 4142 | . . 3 | |
4 | 2, 3 | syl 14 | . 2 |
5 | 1, 4 | mpbiri 167 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wcel 2141 cvv 2730 cun 3119 wss 3121 cif 3526 cpw 3566 |
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-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pr 4194 ax-un 4418 |
This theorem depends on definitions: df-bi 116 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-rab 2457 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-if 3527 df-pw 3568 df-sn 3589 df-pr 3590 df-uni 3797 |
This theorem is referenced by: ifelpwund 4467 ifelpwun 4468 |
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