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Mirrors > Home > ILE Home > Th. List > pmss12g | Unicode version |
Description: Subset relation for the set of partial functions. (Contributed by Mario Carneiro, 31-Dec-2013.) |
Ref | Expression |
---|---|
pmss12g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpss12 4718 | . . . . . . 7 | |
2 | 1 | ancoms 266 | . . . . . 6 |
3 | sstr 3155 | . . . . . . 7 | |
4 | 3 | expcom 115 | . . . . . 6 |
5 | 2, 4 | syl 14 | . . . . 5 |
6 | 5 | anim2d 335 | . . . 4 |
7 | 6 | adantr 274 | . . 3 |
8 | ssexg 4128 | . . . . 5 | |
9 | ssexg 4128 | . . . . 5 | |
10 | elpmg 6642 | . . . . 5 | |
11 | 8, 9, 10 | syl2an 287 | . . . 4 |
12 | 11 | an4s 583 | . . 3 |
13 | elpmg 6642 | . . . 4 | |
14 | 13 | adantl 275 | . . 3 |
15 | 7, 12, 14 | 3imtr4d 202 | . 2 |
16 | 15 | ssrdv 3153 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wcel 2141 cvv 2730 wss 3121 cxp 4609 wfun 5192 (class class class)co 5853 cpm 6627 |
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-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 ax-un 4418 ax-setind 4521 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ne 2341 df-ral 2453 df-rex 2454 df-rab 2457 df-v 2732 df-sbc 2956 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-opab 4051 df-id 4278 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-iota 5160 df-fun 5200 df-fv 5206 df-ov 5856 df-oprab 5857 df-mpo 5858 df-pm 6629 |
This theorem is referenced by: lmres 13042 |
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