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Mirrors > Home > ILE Home > Th. List > sbh | Unicode version |
Description: Substitution for a variable not free in a wff does not affect it. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 17-Oct-2004.) |
Ref | Expression |
---|---|
sbh.1 |
Ref | Expression |
---|---|
sbh |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb1 1746 | . . . 4 | |
2 | sbh.1 | . . . . 5 | |
3 | 2 | 19.41h 1665 | . . . 4 |
4 | 1, 3 | sylib 121 | . . 3 |
5 | 4 | simprd 113 | . 2 |
6 | stdpc4 1755 | . . 3 | |
7 | 2, 6 | syl 14 | . 2 |
8 | 5, 7 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1333 wex 1472 wsb 1742 |
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-4 1490 ax-i9 1510 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-sb 1743 |
This theorem is referenced by: sbf 1757 sb6x 1759 nfs1f 1760 hbs1f 1761 sbid2h 1829 sblimv 1874 sbrim 1936 sbrbif 1942 elsb3 2135 elsb4 2136 |
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