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Mirrors > Home > MPE Home > Th. List > ralab | Structured version Visualization version Unicode version |
Description: Universal quantification over a class abstraction. (Contributed by Jeff Madsen, 10-Jun-2010.) |
Ref | Expression |
---|---|
ralab.1 |
Ref | Expression |
---|---|
ralab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2917 | . 2 | |
2 | vex 3203 | . . . . 5 | |
3 | ralab.1 | . . . . 5 | |
4 | 2, 3 | elab 3350 | . . . 4 |
5 | 4 | imbi1i 339 | . . 3 |
6 | 5 | albii 1747 | . 2 |
7 | 1, 6 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wal 1481 wcel 1990 cab 2608 wral 2912 |
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-v 3202 |
This theorem is referenced by: ralrnmpt2 6775 funcnvuni 7119 kardex 8757 karden 8758 fimaxre3 10970 ptcnp 21425 ptrescn 21442 itg2leub 23501 nmoubi 27627 nmopub 28767 nmfnleub 28784 nmcexi 28885 mblfinlem3 33448 ismblfin 33450 itg2addnc 33464 hbtlem2 37694 |
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