Theorem mdm2i 72

Description: Par is monotone in its second argument. Inference form of mdm2 69. Essentially ax-cut 6 using linear implication.

Hypotheses

Ref	Expression
mdm2i.1	⊦ (𝜑 ⅋ 𝜓)
mdm2i.2	⊦ (𝜓 ⊸ 𝜒)

Assertion

Ref	Expression
mdm2i	⊦ (𝜑 ⅋ 𝜒)

Proof of Theorem mdm2i

Step	Hyp	Ref	Expression
1		mdm2i.1	. . . 4 ⊦ (𝜑 ⅋ 𝜓)
2	1	ax-ibot 4	. . 3 ⊦ (⊥ ⅋ (𝜑 ⅋ 𝜓))
3		mdm2i.2	. . 3 ⊦ (𝜓 ⊸ 𝜒)
4	2, 3	mdm2 69	. 2 ⊦ (⊥ ⅋ (𝜑 ⅋ 𝜒))
5	4	ax-ebot 5	1 ⊦ (𝜑 ⅋ 𝜒)

Syntax hints:  ⊥wbot 1   ⅋ wmd 2   ⊸ 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-eac1 33

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

This theorem is referenced by:  lmp  76  acm1  80