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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 4041 | . 2 | |
2 | csbconstg 3063 | . . 3 | |
3 | 2 | breqd 3998 | . 2 |
4 | 1, 3 | bitrd 187 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wcel 2141 wsbc 2955 csb 3049 class class class wbr 3987 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-sbc 2956 df-csb 3050 df-un 3125 df-sn 3587 df-pr 3588 df-op 3590 df-br 3988 |
This theorem is referenced by: sbcbr1g 4043 sbcbr2g 4044 |
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