Theorem mdm1i 71

Description: Par is monotone in its first argument. Inference form of mdm1 70.

Hypotheses

Ref	Expression
mdm1i.1	⊦ (𝜑 ⅋ 𝜓)
mdm1i.2	⊦ (𝜑 ⊸ 𝜒)

Assertion

Ref	Expression
mdm1i	⊦ (𝜒 ⅋ 𝜓)

Proof of Theorem mdm1i

Step	Hyp	Ref	Expression
1		mdm1i.1	. . . 4 ⊦ (𝜑 ⅋ 𝜓)
2	1	ax-ibot 4	. . 3 ⊦ (⊥ ⅋ (𝜑 ⅋ 𝜓))
3		mdm1i.2	. . 3 ⊦ (𝜑 ⊸ 𝜒)
4	2, 3	mdm1 70	. 2 ⊦ (⊥ ⅋ (𝜒 ⅋ 𝜓))
5	4	ax-ebot 5	1 ⊦ (𝜒 ⅋ 𝜓)

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: (None)