Theorem txprel 36099

Description: A tail Cartesian product is a relationship. (Contributed by Scott Fenton, 31-Mar-2012.)

Assertion

Ref	Expression
txprel	⊢ Rel (𝐴 ⊗ 𝐵)

Proof of Theorem txprel

Step	Hyp	Ref	Expression
1		txpss3v 36098	. . 3 ⊢ (𝐴 ⊗ 𝐵) ⊆ (V × (V × V))
2		xpss 5650	. . 3 ⊢ (V × (V × V)) ⊆ (V × V)
3	1, 2	sstri 3945	. 2 ⊢ (𝐴 ⊗ 𝐵) ⊆ (V × V)
4		df-rel 5641	. 2 ⊢ (Rel (𝐴 ⊗ 𝐵) ↔ (𝐴 ⊗ 𝐵) ⊆ (V × V))
5	3, 4	mpbir 231	1 ⊢ Rel (𝐴 ⊗ 𝐵)

Syntax hints:  Vcvv 3442   ⊆ wss 3903   × cxp 5632  Rel wrel 5639   ⊗ ctxp 36050

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-sep 5245  ax-pr 5381

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-ral 3053  df-rex 3063  df-rab 3402  df-v 3444  df-dif 3906  df-un 3908  df-in 3910  df-ss 3920  df-nul 4288  df-if 4482  df-sn 4583  df-pr 4585  df-op 4589  df-br 5101  df-opab 5163  df-xp 5640  df-rel 5641  df-cnv 5642  df-co 5643  df-res 5646  df-txp 36074

This theorem is referenced by:  pprodss4v  36104