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Mirrors > Home > ILE Home > Th. List > sb5 | Unicode version |
Description: Equivalence for substitution. Similar to Theorem 6.1 of [Quine] p. 40. (Contributed by NM, 18-Aug-1993.) (Revised by NM, 14-Apr-2008.) |
Ref | Expression |
---|---|
sb5 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb6 1873 | . 2 | |
2 | sb56 1872 | . 2 | |
3 | 1, 2 | bitr4i 186 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1340 wex 1479 wsb 1749 |
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 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 |
This theorem depends on definitions: df-bi 116 df-sb 1750 |
This theorem is referenced by: sbnv 1875 sborv 1877 sbi2v 1879 nfsbxy 1929 nfsbxyt 1930 2sb5 1970 dfsb7 1978 sb7f 1979 sbexyz 1990 sbc5 2969 |
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