ax-bdim - Mathbox for BJ

	Mathbox for BJ		< Previous Next > Nearby theorems
Mirrors > Home > ILE Home > Th. List > Mathboxes > ax-bdim		GIF version

Axiom ax-bdim 17062

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 17060	1 wff BOUNDED (𝜑 → 𝜓)

Colors of variables: wff set class

This axiom is used by: bdbi 17074 bdstab 17075 bdth 17079 bdcdeq 17087 bdreu 17103 bdrmo 17104 bdcriota 17131 bj-inf2vnlem3 17220