Theorem txprel 36050

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 36049	. . 3 ⊢ (𝐴 ⊗ 𝐵) ⊆ (V × (V × V))
2		xpss 5639	. . 3 ⊢ (V × (V × V)) ⊆ (V × V)
3	1, 2	sstri 3942	. 2 ⊢ (𝐴 ⊗ 𝐵) ⊆ (V × V)
4		df-rel 5630	. 2 ⊢ (Rel (𝐴 ⊗ 𝐵) ↔ (𝐴 ⊗ 𝐵) ⊆ (V × V))
5	3, 4	mpbir 231	1 ⊢ Rel (𝐴 ⊗ 𝐵)

Syntax hints:  Vcvv 3439   ⊆ wss 3900   × cxp 5621  Rel wrel 5628   ⊗ ctxp 36001

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 2707  ax-sep 5240  ax-nul 5250  ax-pr 5376

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 2714  df-cleq 2727  df-clel 2810  df-ral 3051  df-rex 3060  df-rab 3399  df-v 3441  df-dif 3903  df-un 3905  df-in 3907  df-ss 3917  df-nul 4285  df-if 4479  df-sn 4580  df-pr 4582  df-op 4586  df-br 5098  df-opab 5160  df-xp 5629  df-rel 5630  df-cnv 5631  df-co 5632  df-res 5635  df-txp 36025

This theorem is referenced by:  pprodss4v  36055