Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > sbcbr12g | Unicode version |
Description: Move substitution in and out of a binary relation. (Contributed by NM, 13-Dec-2005.) |
Ref | Expression |
---|---|
sbcbr12g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcbrg 4030 | . 2 | |
2 | csbconstg 3054 | . . 3 | |
3 | 2 | breqd 3987 | . 2 |
4 | 1, 3 | bitrd 187 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wcel 2135 wsbc 2946 csb 3040 class class class wbr 3976 |
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-v 2723 df-sbc 2947 df-csb 3041 df-un 3115 df-sn 3576 df-pr 3577 df-op 3579 df-br 3977 |
This theorem is referenced by: sbcbr1g 4032 sbcbr2g 4033 |
Copyright terms: Public domain | W3C validator |