| Metamath Proof Explorer |
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Related theorems Unicode version |
| Description: Membership of a class abstraction in another class. |
| Ref | Expression |
|---|---|
| clabel |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-clel 2166 |
. 2
| |
| 2 | abeq2 2277 |
. . . . 5
| |
| 3 | 2 | anbi1i 805 |
. . . 4
|
| 4 | ancom 510 |
. . . 4
| |
| 5 | 3, 4 | bitri 306 |
. . 3
|
| 6 | 5 | exbii 1716 |
. 2
|
| 7 | 1, 6 | bitri 306 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem is referenced by: grothprimlem 11169 |
| This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 ax-7 1621 ax-gen 1622 ax-8 1623 ax-10 1625 ax-12 1627 ax-17 1634 ax-4 1637 ax-5o 1639 ax-6o 1642 ax-9o 1792 ax-10o 1810 ax-16 1883 ax-11o 1893 ax-ext 2152 |
| This theorem depends on definitions: df-bi 232 df-an 435 df-ex 1645 df-sb 1845 df-clab 2158 df-cleq 2163 df-clel 2166 |