Axiom ax-bdan 13184

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 103	. 2 wff (𝜑 ∧ 𝜓)
4	3	wbd 13181	1 wff BOUNDED (𝜑 ∧ 𝜓)

This axiom is referenced by:  bdbi  13195  bd3an  13199  bdxor  13205  bdcrab  13221  bdreu  13224  bdcdif  13230  bdcin  13232  bdvsn  13243  bdop  13244  bdeqsuc  13250  bj-bdind  13299