Theorem mdm1 70

Description: Par is monotone in its first argument.

Hypotheses

Ref	Expression
mdm1.1	⊦ (𝜃 ⅋ (𝜑 ⅋ 𝜓))
mdm1.2	⊦ (𝜑 ⊸ 𝜒)

Assertion

Ref	Expression
mdm1	⊦ (𝜃 ⅋ (𝜒 ⅋ 𝜓))

Proof of Theorem mdm1

Step	Hyp	Ref	Expression
1		mdm1.1	. . . 4 ⊦ (𝜃 ⅋ (𝜑 ⅋ 𝜓))
2	1	mdcod 11	. . 3 ⊦ (𝜃 ⅋ (𝜓 ⅋ 𝜑))
3		mdm1.2	. . 3 ⊦ (𝜑 ⊸ 𝜒)
4	2, 3	mdm2 69	. 2 ⊦ (𝜃 ⅋ (𝜓 ⅋ 𝜒))
5	4	mdcod 11	1 ⊦ (𝜃 ⅋ (𝜒 ⅋ 𝜓))

Syntax hints:   ⅋ 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:  mdm1i  71  mdm1s  73