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Mirrors > Home > ILE Home > Th. List > fiss | Unicode version |
Description: Subset relationship for function . (Contributed by Jeff Hankins, 7-Oct-2009.) (Revised by Mario Carneiro, 24-Nov-2013.) |
Ref | Expression |
---|---|
fiss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 110 | . . . 4 | |
2 | sspwb 4210 | . . . . 5 | |
3 | ssrin 3358 | . . . . 5 | |
4 | 2, 3 | sylbi 121 | . . . 4 |
5 | ssrexv 3218 | . . . 4 | |
6 | 1, 4, 5 | 3syl 17 | . . 3 |
7 | vex 2738 | . . . 4 | |
8 | simpl 109 | . . . . 5 | |
9 | 8, 1 | ssexd 4138 | . . . 4 |
10 | elfi 6960 | . . . 4 | |
11 | 7, 9, 10 | sylancr 414 | . . 3 |
12 | elfi 6960 | . . . . 5 | |
13 | 7, 12 | mpan 424 | . . . 4 |
14 | 13 | adantr 276 | . . 3 |
15 | 6, 11, 14 | 3imtr4d 203 | . 2 |
16 | 15 | ssrdv 3159 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 104 wb 105 wceq 1353 wcel 2146 wrex 2454 cvv 2735 cin 3126 wss 3127 cpw 3572 cint 3840 cfv 5208 cfn 6730 cfi 6957 |
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-in1 614 ax-in2 615 ax-io 709 ax-5 1445 ax-7 1446 ax-gen 1447 ax-ie1 1491 ax-ie2 1492 ax-8 1502 ax-10 1503 ax-11 1504 ax-i12 1505 ax-bndl 1507 ax-4 1508 ax-17 1524 ax-i9 1528 ax-ial 1532 ax-i5r 1533 ax-13 2148 ax-14 2149 ax-ext 2157 ax-sep 4116 ax-nul 4124 ax-pow 4169 ax-pr 4203 ax-un 4427 ax-iinf 4581 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1459 df-sb 1761 df-eu 2027 df-mo 2028 df-clab 2162 df-cleq 2168 df-clel 2171 df-nfc 2306 df-ne 2346 df-ral 2458 df-rex 2459 df-v 2737 df-sbc 2961 df-csb 3056 df-dif 3129 df-un 3131 df-in 3133 df-ss 3140 df-nul 3421 df-pw 3574 df-sn 3595 df-pr 3596 df-op 3598 df-uni 3806 df-int 3841 df-br 3999 df-opab 4060 df-mpt 4061 df-id 4287 df-suc 4365 df-iom 4584 df-xp 4626 df-rel 4627 df-cnv 4628 df-co 4629 df-dm 4630 df-rn 4631 df-res 4632 df-ima 4633 df-iota 5170 df-fun 5210 df-fn 5211 df-f 5212 df-f1 5213 df-fo 5214 df-f1o 5215 df-fv 5216 df-er 6525 df-en 6731 df-fin 6733 df-fi 6958 |
This theorem is referenced by: (None) |
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