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Mirrors > Home > ILE Home > Th. List > fabexg | Unicode version |
Description: Existence of a set of functions. (Contributed by Paul Chapman, 25-Feb-2008.) |
Ref | Expression |
---|---|
fabexg.1 |
Ref | Expression |
---|---|
fabexg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpexg 4699 | . 2 | |
2 | pwexg 4141 | . 2 | |
3 | fabexg.1 | . . . . 5 | |
4 | fssxp 5336 | . . . . . . . 8 | |
5 | velpw 3550 | . . . . . . . 8 | |
6 | 4, 5 | sylibr 133 | . . . . . . 7 |
7 | 6 | anim1i 338 | . . . . . 6 |
8 | 7 | ss2abi 3200 | . . . . 5 |
9 | 3, 8 | eqsstri 3160 | . . . 4 |
10 | ssab2 3212 | . . . 4 | |
11 | 9, 10 | sstri 3137 | . . 3 |
12 | ssexg 4103 | . . 3 | |
13 | 11, 12 | mpan 421 | . 2 |
14 | 1, 2, 13 | 3syl 17 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wcel 2128 cab 2143 cvv 2712 wss 3102 cpw 3543 cxp 4583 wf 5165 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 ax-un 4393 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-opab 4026 df-xp 4591 df-rel 4592 df-cnv 4593 df-dm 4595 df-rn 4596 df-fun 5171 df-fn 5172 df-f 5173 |
This theorem is referenced by: fabex 5357 f1oabexg 5425 |
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