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Mirrors > Home > ILE Home > Th. List > sbcth | Unicode version |
Description: A substitution into a theorem remains true (when is a set). (Contributed by NM, 5-Nov-2005.) |
Ref | Expression |
---|---|
sbcth.1 |
Ref | Expression |
---|---|
sbcth |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcth.1 | . . 3 | |
2 | 1 | ax-gen 1429 | . 2 |
3 | spsbc 2948 | . 2 | |
4 | 2, 3 | mpi 15 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1333 wcel 2128 wsbc 2937 |
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-5 1427 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-v 2714 df-sbc 2938 |
This theorem is referenced by: rabrsndc 3628 iota4an 5155 |
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