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Mirrors > Home > ILE Home > Th. List > sbcbi2 | Unicode version |
Description: Substituting into equivalent wff's gives equivalent results. (Contributed by Giovanni Mascellani, 9-Apr-2018.) |
Ref | Expression |
---|---|
sbcbi2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | abbi 2192 | . . 3 | |
2 | eleq2 2142 | . . 3 | |
3 | 1, 2 | sylbi 119 | . 2 |
4 | df-sbc 2816 | . 2 | |
5 | df-sbc 2816 | . 2 | |
6 | 3, 4, 5 | 3bitr4g 221 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wal 1282 wceq 1284 wcel 1433 cab 2067 wsbc 2815 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-sbc 2816 |
This theorem is referenced by: (None) |
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