Theorem licond 95

Description: Deduction form of licon 94.

Hypothesis

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

Assertion

Ref	Expression
licond	⊦ (𝜒 ⅋ (~ 𝜓 ⊸ ~ 𝜑))

Proof of Theorem licond

Step	Hyp	Ref	Expression
1		licond.1	. . . . . . 7 ⊦ (𝜒 ⅋ (𝜑 ⊸ 𝜓))
2	1	dfli1 63	. . . . . 6 ⊦ (𝜒 ⅋ (~ 𝜑 ⅋ 𝜓))
3	2	mdasri 17	. . . . 5 ⊦ ((𝜒 ⅋ ~ 𝜑) ⅋ 𝜓)
4	3	dnid 23	. . . 4 ⊦ ((𝜒 ⅋ ~ 𝜑) ⅋ ~ ~ 𝜓)
5	4	mdasi 14	. . 3 ⊦ (𝜒 ⅋ (~ 𝜑 ⅋ ~ ~ 𝜓))
6	5	mdcod 11	. 2 ⊦ (𝜒 ⅋ (~ ~ 𝜓 ⅋ ~ 𝜑))
7	6	dfli2 64	1 ⊦ (𝜒 ⅋ (~ 𝜓 ⊸ ~ 𝜑))

Syntax hints:   ⅋ wmd 2  ~ wneg 3   ⊸ 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)