Theorem bdxor 10627

Description: The exclusive disjunction of two bounded formulas is bounded. (Contributed by BJ, 3-Oct-2019.)

Hypotheses

Ref	Expression
bdxor.1	|- BOUNDED ph
bdxor.2	|- BOUNDED ps

Assertion

Ref	Expression
bdxor	|- BOUNDED ( ph \/_ ps )

Proof of Theorem bdxor

Step	Hyp	Ref	Expression
1		bdxor.1	. . . 4 |- BOUNDED ph
2		bdxor.2	. . . 4 |- BOUNDED ps
3	1, 2	ax-bdor 10607	. . 3 |- BOUNDED ( ph \/ ps )
4	1, 2	ax-bdan 10606	. . . 4 |- BOUNDED ( ph /\ ps )
5	4	ax-bdn 10608	. . 3 |- BOUNDED -. ( ph /\ ps )
6	3, 5	ax-bdan 10606	. 2 |- BOUNDED ( ( ph \/ ps ) /\ -. ( ph /\ ps ) )
7		df-xor 1307	. 2 |- ( ( ph \/_ ps ) <-> ( ( ph \/ ps ) /\ -. ( ph /\ ps ) ) )
8	6, 7	bd0r 10616	1 |- BOUNDED ( ph \/_ ps )

Syntax hints:   -. wn 3   /\ wa 102   \/ wo 661   \/_ wxo 1306  BOUNDED wbd 10603

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-bd0 10604  ax-bdan 10606  ax-bdor 10607  ax-bdn 10608

This theorem depends on definitions:  df-bi 115  df-xor 1307

This theorem is referenced by: (None)