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Mirrors > Home > ILE Home > Th. List > acexmidlema | Unicode version |
Description: Lemma for acexmid 5849. (Contributed by Jim Kingdon, 6-Aug-2019.) |
Ref | Expression |
---|---|
acexmidlem.a | |
acexmidlem.b | |
acexmidlem.c |
Ref | Expression |
---|---|
acexmidlema |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | acexmidlem.a | . . . 4 | |
2 | 1 | eleq2i 2237 | . . 3 |
3 | p0ex 4172 | . . . . 5 | |
4 | 3 | prid2 3688 | . . . 4 |
5 | eqeq1 2177 | . . . . . 6 | |
6 | 5 | orbi1d 786 | . . . . 5 |
7 | 6 | elrab3 2887 | . . . 4 |
8 | 4, 7 | ax-mp 5 | . . 3 |
9 | 2, 8 | bitri 183 | . 2 |
10 | noel 3418 | . . . 4 | |
11 | 0ex 4114 | . . . . . 6 | |
12 | 11 | snid 3612 | . . . . 5 |
13 | eleq2 2234 | . . . . 5 | |
14 | 12, 13 | mpbii 147 | . . . 4 |
15 | 10, 14 | mto 657 | . . 3 |
16 | orel1 720 | . . 3 | |
17 | 15, 16 | ax-mp 5 | . 2 |
18 | 9, 17 | sylbi 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wo 703 wceq 1348 wcel 2141 crab 2452 c0 3414 csn 3581 cpr 3582 |
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-14 2144 ax-ext 2152 ax-sep 4105 ax-nul 4113 ax-pow 4158 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rab 2457 df-v 2732 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-nul 3415 df-pw 3566 df-sn 3587 df-pr 3588 |
This theorem is referenced by: acexmidlem1 5846 |
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