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Mirrors > Home > ILE Home > Th. List > sbequ8 | Unicode version |
Description: Elimination of equality from antecedent after substitution. (Contributed by NM, 5-Aug-1993.) (Proof revised by Jim Kingdon, 20-Jan-2018.) |
Ref | Expression |
---|---|
sbequ8 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.4 238 | . . 3 | |
2 | simpl 102 | . . . . . 6 | |
3 | pm3.35 329 | . . . . . 6 | |
4 | 2, 3 | jca 290 | . . . . 5 |
5 | simpl 102 | . . . . . 6 | |
6 | pm3.4 316 | . . . . . 6 | |
7 | 5, 6 | jca 290 | . . . . 5 |
8 | 4, 7 | impbii 117 | . . . 4 |
9 | 8 | exbii 1496 | . . 3 |
10 | 1, 9 | anbi12i 433 | . 2 |
11 | df-sb 1646 | . 2 | |
12 | df-sb 1646 | . 2 | |
13 | 10, 11, 12 | 3bitr4ri 202 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wex 1381 wsb 1645 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-sb 1646 |
This theorem is referenced by: sbidm 1731 |
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