Axiom ax-bdan 11175

Description: The conjunction of two bounded formulas is bounded. (Contributed by BJ, 25-Sep-2019.)

Hypotheses

Ref	Expression
bdim.1	⊢ BOUNDED 𝜑
bdim.2	⊢ BOUNDED 𝜓

Assertion

Ref	Expression
ax-bdan	⊢ BOUNDED (𝜑 ∧ 𝜓)

Detailed syntax breakdown of Axiom ax-bdan

Step	Hyp	Ref	Expression
1		wph	. . 3 wff 𝜑
2		wps	. . 3 wff 𝜓
3	1, 2	wa 102	. 2 wff (𝜑 ∧ 𝜓)
4	3	wbd 11172	1 wff BOUNDED (𝜑 ∧ 𝜓)

This axiom is referenced by:  bdbi  11186  bd3an  11190  bdxor  11196  bdcrab  11212  bdreu  11215  bdcdif  11221  bdcin  11223  bdvsn  11234  bdop  11235  bdeqsuc  11241  bj-bdind  11294