Theorem mdas 110

Description: ⅋ is associative.

Assertion

Ref	Expression
mdas	⊦ (((𝜑 ⅋ 𝜓) ⅋ 𝜒) ⊸ (𝜑 ⅋ (𝜓 ⅋ 𝜒)))

Proof of Theorem mdas

Step	Hyp	Ref	Expression
1		ax-mdas 9	. 2 ⊦ (~ ((𝜑 ⅋ 𝜓) ⅋ 𝜒) ⅋ (𝜑 ⅋ (𝜓 ⅋ 𝜒)))
2	1	dfli2i 66	1 ⊦ (((𝜑 ⅋ 𝜓) ⅋ 𝜒) ⊸ (𝜑 ⅋ (𝜓 ⅋ 𝜒)))

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  ax-eac2 34

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

This theorem is referenced by: (None)