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Mirrors > Home > MPE Home > Th. List > eq2tri | Structured version Visualization version 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 466 | . 2 | |
2 | eq2tr.1 | . . . 4 | |
3 | 2 | eqeq2d 2632 | . . 3 |
4 | 3 | pm5.32i 669 | . 2 |
5 | eq2tr.2 | . . . 4 | |
6 | 5 | eqeq2d 2632 | . . 3 |
7 | 6 | pm5.32i 669 | . 2 |
8 | 1, 4, 7 | 3bitr3i 290 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 df-cleq 2615 |
This theorem is referenced by: xpassen 8054 |
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