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Theorem brxp 4298
Description: Binary relation on a cross product. (Contributed by NM, 22-Apr-2004.)
Assertion
Ref Expression
brxp (A(𝐶 × 𝐷)B ↔ (A 𝐶 B 𝐷))

Proof of Theorem brxp
StepHypRef Expression
1 df-br 3735 . 2 (A(𝐶 × 𝐷)B ↔ ⟨A, B (𝐶 × 𝐷))
2 opelxp 4297 . 2 (⟨A, B (𝐶 × 𝐷) ↔ (A 𝐶 B 𝐷))
31, 2bitri 173 1 (A(𝐶 × 𝐷)B ↔ (A 𝐶 B 𝐷))
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98   wcel 1370  cop 3349   class class class wbr 3734   × cxp 4266
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-14 1382  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000  ax-sep 3845  ax-pow 3897  ax-pr 3914
This theorem depends on definitions:  df-bi 110  df-3an 873  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-ral 2285  df-rex 2286  df-v 2533  df-un 2895  df-in 2897  df-ss 2904  df-pw 3332  df-sn 3352  df-pr 3353  df-op 3355  df-br 3735  df-opab 3789  df-xp 4274
This theorem is referenced by:  brrelex12  4304  brel  4315  brinxp2  4330  eqbrrdva  4428  xpidtr  4638  xpcom  4787  tpostpos  5797  swoer  6041  erinxp  6087  ecopover  6111  ecopoverg  6114  ltxrlt  6687
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