Axiom ax-bdim 13335

Description: An implication between 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-bdim	⊢ BOUNDED (𝜑 → 𝜓)

Detailed syntax breakdown of Axiom ax-bdim

Step	Hyp	Ref	Expression
1		wph	. . 3 wff 𝜑
2		wps	. . 3 wff 𝜓
3	1, 2	wi 4	. 2 wff (𝜑 → 𝜓)
4	3	wbd 13333	1 wff BOUNDED (𝜑 → 𝜓)

This axiom is referenced by:  bdbi  13347  bdstab  13348  bdth  13352  bdcdeq  13360  bdreu  13376  bdrmo  13377  bdcriota  13404  bj-inf2vnlem3  13493