Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > sbcnestg | Unicode version |
Description: Nest the composition of two substitutions. (Contributed by NM, 27-Nov-2005.) (Proof shortened by Mario Carneiro, 11-Nov-2016.) |
Ref | Expression |
---|---|
sbcnestg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1508 | . . 3 | |
2 | 1 | ax-gen 1425 | . 2 |
3 | sbcnestgf 3046 | . 2 | |
4 | 2, 3 | mpan2 421 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1329 wnf 1436 wcel 1480 wsbc 2904 csb 2998 |
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 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-sbc 2905 df-csb 2999 |
This theorem is referenced by: sbcco3g 3052 |
Copyright terms: Public domain | W3C validator |