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Mirrors > Home > NFE Home > Th. List > rextpg | Unicode version |
Description: Convert a quantification over a triple to a disjunction. (Contributed by Mario Carneiro, 23-Apr-2015.) |
Ref | Expression |
---|---|
ralprg.1 | |
ralprg.2 | |
raltpg.3 |
Ref | Expression |
---|---|
rextpg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralprg.1 | . . . . . 6 | |
2 | ralprg.2 | . . . . . 6 | |
3 | 1, 2 | rexprg 3776 | . . . . 5 |
4 | 3 | orbi1d 683 | . . . 4 |
5 | raltpg.3 | . . . . . 6 | |
6 | 5 | rexsng 3766 | . . . . 5 |
7 | 6 | orbi2d 682 | . . . 4 |
8 | 4, 7 | sylan9bb 680 | . . 3 |
9 | 8 | 3impa 1146 | . 2 |
10 | df-tp 3743 | . . . 4 | |
11 | 10 | rexeqi 2812 | . . 3 |
12 | rexun 3443 | . . 3 | |
13 | 11, 12 | bitri 240 | . 2 |
14 | df-3or 935 | . 2 | |
15 | 9, 13, 14 | 3bitr4g 279 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wo 357 wa 358 w3o 933 w3a 934 wceq 1642 wcel 1710 wrex 2615 cun 3207 csn 3737 cpr 3738 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: rextp 3782 |
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