Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > breqtrri | GIF version |
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
breqtrr.1 | ⊢ 𝐴𝑅𝐵 |
breqtrr.2 | ⊢ 𝐶 = 𝐵 |
Ref | Expression |
---|---|
breqtrri | ⊢ 𝐴𝑅𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breqtrr.1 | . 2 ⊢ 𝐴𝑅𝐵 | |
2 | breqtrr.2 | . . 3 ⊢ 𝐶 = 𝐵 | |
3 | 2 | eqcomi 2161 | . 2 ⊢ 𝐵 = 𝐶 |
4 | 1, 3 | breqtri 3990 | 1 ⊢ 𝐴𝑅𝐶 |
Colors of variables: wff set class |
Syntax hints: = wceq 1335 class class class wbr 3966 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-sn 3566 df-pr 3567 df-op 3569 df-br 3967 |
This theorem is referenced by: 3brtr4i 3995 ensn1 6742 pw1dom2 7163 0lt1sr 7686 0le2 8924 2pos 8925 3pos 8928 4pos 8931 5pos 8934 6pos 8935 7pos 8936 8pos 8937 9pos 8938 1lt2 9003 2lt3 9004 3lt4 9006 4lt5 9009 5lt6 9013 6lt7 9018 7lt8 9024 8lt9 9031 nn0le2xi 9141 numltc 9321 declti 9333 sqge0i 10509 faclbnd2 10620 ege2le3 11572 cos2bnd 11661 3dvdsdec 11760 n2dvdsm1 11808 n2dvds3 11810 dveflem 13129 tangtx 13201 ex-fl 13343 |
Copyright terms: Public domain | W3C validator |