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Mirrors > Home > MPE Home > Th. List > ectocld | Structured version Visualization version Unicode version |
Description: Implicit substitution of class for equivalence class. (Contributed by Mario Carneiro, 9-Jul-2014.) |
Ref | Expression |
---|---|
ectocl.1 | |
ectocl.2 | |
ectocld.3 |
Ref | Expression |
---|---|
ectocld |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ectocld.3 | . . . 4 | |
2 | ectocl.2 | . . . . 5 | |
3 | 2 | eqcoms 2630 | . . . 4 |
4 | 1, 3 | syl5ibcom 235 | . . 3 |
5 | 4 | rexlimdva 3031 | . 2 |
6 | elqsi 7800 | . . 3 | |
7 | ectocl.1 | . . 3 | |
8 | 6, 7 | eleq2s 2719 | . 2 |
9 | 5, 8 | impel 485 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 wrex 2913 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: ectocl 7815 elqsn0 7816 qsdisj 7824 qsel 7826 eqgen 17647 orbsta 17746 sylow1lem3 18015 sylow2alem2 18033 sylow2a 18034 sylow2blem2 18036 frgpup1 18188 frgpup3lem 18190 quscrng 19240 pi1xfr 22855 pi1coghm 22861 vitalilem3 23379 |
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