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Mirrors > Home > ILE Home > Th. List > preq1 | Unicode version |
Description: Equality theorem for unordered pairs. (Contributed by NM, 29-Mar-1998.) |
Ref | Expression |
---|---|
preq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sneq 3592 | . . 3 | |
2 | 1 | uneq1d 3280 | . 2 |
3 | df-pr 3588 | . 2 | |
4 | df-pr 3588 | . 2 | |
5 | 2, 3, 4 | 3eqtr4g 2228 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 cun 3119 csn 3581 cpr 3582 |
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 |
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-v 2732 df-un 3125 df-sn 3587 df-pr 3588 |
This theorem is referenced by: preq2 3659 preq12 3660 preq1i 3661 preq1d 3664 tpeq1 3667 prnzg 3705 preq12b 3755 preq12bg 3758 opeq1 3763 uniprg 3809 intprg 3862 prexg 4194 opthreg 4538 bdxmet 13260 bj-prexg 13911 |
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