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Mirrors > Home > NFE Home > Th. List > 3reeanv | Unicode version |
Description: Rearrange three existential quantifiers. (Contributed by Jeff Madsen, 11-Jun-2010.) |
Ref | Expression |
---|---|
3reeanv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.41v 2764 | . . 3 | |
2 | reeanv 2778 | . . . 4 | |
3 | 2 | anbi1i 676 | . . 3 |
4 | 1, 3 | bitri 240 | . 2 |
5 | df-3an 936 | . . . . 5 | |
6 | 5 | 2rexbii 2641 | . . . 4 |
7 | reeanv 2778 | . . . 4 | |
8 | 6, 7 | bitri 240 | . . 3 |
9 | 8 | rexbii 2639 | . 2 |
10 | df-3an 936 | . 2 | |
11 | 4, 9, 10 | 3bitr4i 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wa 358 w3a 934 wrex 2615 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-cleq 2346 df-clel 2349 df-nfc 2478 df-rex 2620 |
This theorem is referenced by: xpassen 6057 |
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