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Mirrors > Home > ILE Home > Th. List > nfimad | Unicode version |
Description: Deduction version of bound-variable hypothesis builder nfima 4889. (Contributed by FL, 15-Dec-2006.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
nfimad.2 | |
nfimad.3 |
Ref | Expression |
---|---|
nfimad |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfaba1 2287 | . . 3 | |
2 | nfaba1 2287 | . . 3 | |
3 | 1, 2 | nfima 4889 | . 2 |
4 | nfimad.2 | . . 3 | |
5 | nfimad.3 | . . 3 | |
6 | nfnfc1 2284 | . . . . 5 | |
7 | nfnfc1 2284 | . . . . 5 | |
8 | 6, 7 | nfan 1544 | . . . 4 |
9 | abidnf 2852 | . . . . . 6 | |
10 | 9 | imaeq1d 4880 | . . . . 5 |
11 | abidnf 2852 | . . . . . 6 | |
12 | 11 | imaeq2d 4881 | . . . . 5 |
13 | 10, 12 | sylan9eq 2192 | . . . 4 |
14 | 8, 13 | nfceqdf 2280 | . . 3 |
15 | 4, 5, 14 | syl2anc 408 | . 2 |
16 | 3, 15 | mpbii 147 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wcel 1480 cab 2125 wnfc 2268 cima 4542 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rab 2425 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 df-xp 4545 df-cnv 4547 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 |
This theorem is referenced by: (None) |
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