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Mirrors > Home > ILE Home > Th. List > sstr2 | Unicode version |
Description: Transitivity of subclasses. Exercise 5 of [TakeutiZaring] p. 17. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) |
Ref | Expression |
---|---|
sstr2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3149 |
. . . 4
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2 | 1 | imim1d 75 |
. . 3
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3 | 2 | alimdv 1879 |
. 2
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4 | dfss2 3144 |
. 2
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5 | dfss2 3144 |
. 2
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6 | 3, 4, 5 | 3imtr4g 205 |
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-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-in 3135 df-ss 3142 |
This theorem is referenced by: sstr 3163 sstri 3164 sseq1 3178 sseq2 3179 ssun3 3300 ssun4 3301 ssinss1 3364 ssdisj 3479 triun 4114 trintssm 4117 sspwb 4216 exss 4227 relss 4713 funss 5235 funimass2 5294 fss 5377 fiintim 6927 sbthlem2 6956 sbthlemi3 6957 sbthlemi6 6960 tgss 13499 tgcl 13500 tgss3 13514 clsss 13554 neiss 13586 ssnei2 13593 cnpnei 13655 cnptopco 13658 cnptoprest 13675 txcnp 13707 neibl 13927 metcnp3 13947 bj-nntrans 14639 |
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