Theorem dfli1i 65

Description: Convert from linear implication. Inference for dfli1 63.

Hypothesis

Ref	Expression
dfli1i.1	⊦ (𝜓 ⊸ 𝜒)

Assertion

Ref	Expression
dfli1i	⊦ (~ 𝜓 ⅋ 𝜒)

Proof of Theorem dfli1i

Step	Hyp	Ref	Expression
1		dfli1i.1	. . . 4 ⊦ (𝜓 ⊸ 𝜒)
2	1	ax-ibot 4	. . 3 ⊦ (⊥ ⅋ (𝜓 ⊸ 𝜒))
3	2	dfli1 63	. 2 ⊦ (⊥ ⅋ (~ 𝜓 ⅋ 𝜒))
4	3	ax-ebot 5	1 ⊦ (~ 𝜓 ⅋ 𝜒)

Syntax hints:  ⊥wbot 1   ⅋ 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-eac1 33

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

This theorem is referenced by:  lb1s  67  lb2s  68  nems  86  dflb1s  91  licon  94  ilbd  97  lbsymd  102