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Mirrors > Home > ILE Home > Th. List > eq2tri | Unicode version |
Description: A compound transitive inference for class equality. (Contributed by NM, 22-Jan-2004.) |
Ref | Expression |
---|---|
eq2tr.1 | |
eq2tr.2 |
Ref | Expression |
---|---|
eq2tri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancom 253 | . 2 | |
2 | eq2tr.1 | . . . 4 | |
3 | 2 | eqeq2d 2051 | . . 3 |
4 | 3 | pm5.32i 427 | . 2 |
5 | eq2tr.2 | . . . 4 | |
6 | 5 | eqeq2d 2051 | . . 3 |
7 | 6 | pm5.32i 427 | . 2 |
8 | 1, 4, 7 | 3bitr3i 199 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 |
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-4 1400 ax-17 1419 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-cleq 2033 |
This theorem is referenced by: xpassen 6304 |
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