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Mirrors > Home > ILE Home > Th. List > eqbrtrri | GIF version |
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
eqbrtrr.1 | ⊢ 𝐴 = 𝐵 |
eqbrtrr.2 | ⊢ 𝐴𝑅𝐶 |
Ref | Expression |
---|---|
eqbrtrri | ⊢ 𝐵𝑅𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqbrtrr.1 | . . 3 ⊢ 𝐴 = 𝐵 | |
2 | 1 | eqcomi 2087 | . 2 ⊢ 𝐵 = 𝐴 |
3 | eqbrtrr.2 | . 2 ⊢ 𝐴𝑅𝐶 | |
4 | 2, 3 | eqbrtri 3830 | 1 ⊢ 𝐵𝑅𝐶 |
Colors of variables: wff set class |
Syntax hints: = wceq 1285 class class class wbr 3811 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-v 2614 df-un 2988 df-sn 3428 df-pr 3429 df-op 3431 df-br 3812 |
This theorem is referenced by: 3brtr3i 3838 dju1p1e2 6726 expnass 9896 sqrt2gt1lt2 10309 |
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