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Mirrors > Home > NFE Home > Th. List > rextp | Unicode version |
Description: Convert a quantification over a triple to a disjunction. (Contributed by Mario Carneiro, 23-Apr-2015.) |
Ref | Expression |
---|---|
raltp.1 | |
raltp.2 | |
raltp.3 | |
raltp.4 | |
raltp.5 | |
raltp.6 |
Ref | Expression |
---|---|
rextp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raltp.1 | . 2 | |
2 | raltp.2 | . 2 | |
3 | raltp.3 | . 2 | |
4 | raltp.4 | . . 3 | |
5 | raltp.5 | . . 3 | |
6 | raltp.6 | . . 3 | |
7 | 4, 5, 6 | rextpg 3778 | . 2 |
8 | 1, 2, 3, 7 | mp3an 1277 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 w3o 933 wceq 1642 wcel 1710 wrex 2615 cvv 2859 ctp 3739 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 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-3or 935 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-rex 2620 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-un 3214 df-sn 3741 df-pr 3742 df-tp 3743 |
This theorem is referenced by: (None) |
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