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Mirrors > Home > NFE Home > Th. List > adj11 | Unicode version |
Description: Adjoining a new element is one-to-one. (Contributed by SF, 29-Jan-2015.) |
Ref | Expression |
---|---|
adj11 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | difeq1 3246 | . . . 4 | |
2 | difun2 3629 | . . . 4 | |
3 | difun2 3629 | . . . 4 | |
4 | 1, 2, 3 | 3eqtr3g 2408 | . . 3 |
5 | difsn 3845 | . . . 4 | |
6 | difsn 3845 | . . . 4 | |
7 | 5, 6 | eqeqan12d 2368 | . . 3 |
8 | 4, 7 | syl5ib 210 | . 2 |
9 | uneq1 3411 | . 2 | |
10 | 8, 9 | impbid1 194 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 176 wa 358 wceq 1642 wcel 1710 cdif 3206 cun 3207 csn 3737 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-ss 3259 df-nul 3551 df-sn 3741 |
This theorem is referenced by: nnadjoin 4520 |
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