Theorem bj-xpexg2 37624

Description: Curried (exported) form of xpexg 7747. (Contributed by BJ, 2-Apr-2019.)

Assertion

Ref	Expression
bj-xpexg2	⊢ (𝐴 ∈ 𝑉 → (𝐵 ∈ 𝑊 → (𝐴 × 𝐵) ∈ V))

Proof of Theorem bj-xpexg2

Step	Hyp	Ref	Expression
1		xpexg 7747	. 2 ⊢ ((𝐴 ∈ 𝑉 ∧ 𝐵 ∈ 𝑊) → (𝐴 × 𝐵) ∈ V)
2	1	ex 417	1 ⊢ (𝐴 ∈ 𝑉 → (𝐵 ∈ 𝑊 → (𝐴 × 𝐵) ∈ V))

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2142  Vcvv 3454   × cxp 5658

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-ext 2734  ax-sep 5256  ax-pow 5335  ax-pr 5403  ax-un 7734

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1104  df-tru 1572  df-fal 1582  df-ex 1809  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-ral 3079  df-rex 3089  df-rab 3416  df-v 3456  df-dif 3907  df-un 3909  df-in 3911  df-ss 3921  df-nul 4286  df-if 4487  df-pw 4563  df-sn 4589  df-pr 4591  df-op 4595  df-uni 4872  df-opab 5173  df-xp 5666  df-rel 5667

This theorem is used by:  bj-xpnzexb  37625  bj-xtagex  37653