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Mirrors > Home > MPE Home > Th. List > ectocl | Structured version Visualization version Unicode version |
Description: Implicit substitution of class for equivalence class. (Contributed by NM, 23-Jul-1995.) (Revised by Mario Carneiro, 9-Jul-2014.) |
Ref | Expression |
---|---|
ectocl.1 | |
ectocl.2 | |
ectocl.3 |
Ref | Expression |
---|---|
ectocl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1487 | . 2 | |
2 | ectocl.1 | . . 3 | |
3 | ectocl.2 | . . 3 | |
4 | ectocl.3 | . . . 4 | |
5 | 4 | adantl 482 | . . 3 |
6 | 2, 3, 5 | ectocld 7814 | . 2 |
7 | 1, 6 | mpan 706 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wceq 1483 wtru 1484 wcel 1990 cec 7740 cqs 7741 |
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-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-v 3202 df-qs 7748 |
This theorem is referenced by: vitalilem2 23378 |
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