Theorem inex3 34106

Description: More general sethood condition for the intersection relation. (Contributed by Peter Mazsa, 24-Nov-2019.)

Assertion

Ref	Expression
inex3	|- ( ( A e. V \/ B e. W ) -> ( A i^i B ) e. _V )

Proof of Theorem inex3

Step	Hyp	Ref	Expression
1		inex1g 4801	. 2 |- ( A e. V -> ( A i^i B ) e. _V )
2		inex2ALTV 34105	. 2 |- ( B e. W -> ( A i^i B ) e. _V )
3	1, 2	jaoi 394	1 |- ( ( A e. V \/ B e. W ) -> ( A i^i B ) e. _V )

Syntax hints:   -> wi 4   \/ wo 383   e. wcel 1990   _Vcvv 3200   i^i cin 3573

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-sep 4781

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-in 3581

This theorem is referenced by: (None)