Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > sbcralt | Unicode version |
Description: Interchange class substitution and restricted quantifier. (Contributed by NM, 1-Mar-2008.) (Revised by David Abernethy, 22-Feb-2010.) |
Ref | Expression |
---|---|
sbcralt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcco 2967 | . 2 | |
2 | simpl 108 | . . 3 | |
3 | sbsbc 2950 | . . . . 5 | |
4 | nfcv 2306 | . . . . . . 7 | |
5 | nfs1v 1926 | . . . . . . 7 | |
6 | 4, 5 | nfralxy 2502 | . . . . . 6 |
7 | sbequ12 1758 | . . . . . . 7 | |
8 | 7 | ralbidv 2464 | . . . . . 6 |
9 | 6, 8 | sbie 1778 | . . . . 5 |
10 | 3, 9 | bitr3i 185 | . . . 4 |
11 | nfnfc1 2309 | . . . . . . 7 | |
12 | nfcvd 2307 | . . . . . . . 8 | |
13 | id 19 | . . . . . . . 8 | |
14 | 12, 13 | nfeqd 2321 | . . . . . . 7 |
15 | 11, 14 | nfan1 1551 | . . . . . 6 |
16 | dfsbcq2 2949 | . . . . . . 7 | |
17 | 16 | adantl 275 | . . . . . 6 |
18 | 15, 17 | ralbid 2462 | . . . . 5 |
19 | 18 | adantll 468 | . . . 4 |
20 | 10, 19 | syl5bb 191 | . . 3 |
21 | 2, 20 | sbcied 2982 | . 2 |
22 | 1, 21 | bitr3id 193 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1342 wsb 1749 wcel 2135 wnfc 2293 wral 2442 wsbc 2946 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-v 2723 df-sbc 2947 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |