ax-bdim - Mathbox for BJ

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Axiom ax-bdim 16852

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 16850	1 wff BOUNDED (𝜑 → 𝜓)

Colors of variables: wff set class

This axiom is used by: bdbi 16864 bdstab 16865 bdth 16869 bdcdeq 16877 bdreu 16893 bdrmo 16894 bdcriota 16921 bj-inf2vnlem3 17010