Theorem acm2i 83

Description: With is monotone in its second argument. Inference form of acm2 81.

Hypotheses

Ref	Expression
acm2i.1	⊦ (𝜑 & 𝜓)
acm2i.2	⊦ (𝜓 ⊸ 𝜒)

Assertion

Ref	Expression
acm2i	⊦ (𝜑 & 𝜒)

Proof of Theorem acm2i

Step	Hyp	Ref	Expression
1		acm2i.1	. . . 4 ⊦ (𝜑 & 𝜓)
2	1	ax-ibot 4	. . 3 ⊦ (⊥ ⅋ (𝜑 & 𝜓))
3		acm2i.2	. . 3 ⊦ (𝜓 ⊸ 𝜒)
4	2, 3	acm2 81	. 2 ⊦ (⊥ ⅋ (𝜑 & 𝜒))
5	4	ax-ebot 5	1 ⊦ (𝜑 & 𝜒)

Syntax hints:  ⊥wbot 1   & wac 30   ⊸ wli 61

This theorem was proved from axioms:  ax-ibot 4  ax-ebot 5  ax-cut 6  ax-init 7  ax-mdco 8  ax-mdas 9  ax-iac 32  ax-eac1 33  ax-eac2 34

This theorem depends on definitions:  df-lb 56  df-li 62

This theorem is referenced by: (None)