ax-bdim - Mathbox for BJ

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Axiom ax-bdim 15460

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 15458	1 wff BOUNDED (𝜑 → 𝜓)

Colors of variables: wff set class

This axiom is referenced by: bdbi 15472 bdstab 15473 bdth 15477 bdcdeq 15485 bdreu 15501 bdrmo 15502 bdcriota 15529 bj-inf2vnlem3 15618