Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > csbnestgf | Unicode version |
Description: Nest the composition of two substitutions. (Contributed by NM, 23-Nov-2005.) (Proof shortened by Mario Carneiro, 10-Nov-2016.) |
Ref | Expression |
---|---|
csbnestgf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2671 | . . 3 | |
2 | df-csb 2976 | . . . . . . 7 | |
3 | 2 | abeq2i 2228 | . . . . . 6 |
4 | 3 | sbcbii 2940 | . . . . 5 |
5 | nfcr 2250 | . . . . . . 7 | |
6 | 5 | alimi 1416 | . . . . . 6 |
7 | sbcnestgf 3021 | . . . . . 6 | |
8 | 6, 7 | sylan2 284 | . . . . 5 |
9 | 4, 8 | syl5bb 191 | . . . 4 |
10 | 9 | abbidv 2235 | . . 3 |
11 | 1, 10 | sylan 281 | . 2 |
12 | df-csb 2976 | . 2 | |
13 | df-csb 2976 | . 2 | |
14 | 11, 12, 13 | 3eqtr4g 2175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1314 wceq 1316 wnf 1421 wcel 1465 cab 2103 wnfc 2245 cvv 2660 wsbc 2882 csb 2975 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-sbc 2883 df-csb 2976 |
This theorem is referenced by: csbnestg 3024 csbnest1g 3025 |
Copyright terms: Public domain | W3C validator |