Theorem dfli1 63

Description: Convert from linear implication.

Hypothesis

Ref	Expression
dfli1.1	⊦ (𝜑 ⅋ (𝜓 ⊸ 𝜒))

Assertion

Ref	Expression
dfli1	⊦ (𝜑 ⅋ (~ 𝜓 ⅋ 𝜒))

Proof of Theorem dfli1

Step	Hyp	Ref	Expression
1		dfli1.1	. 2 ⊦ (𝜑 ⅋ (𝜓 ⊸ 𝜒))
2		df-li 62	. 2 ⊦ ((𝜓 ⊸ 𝜒) ⧟ (~ 𝜓 ⅋ 𝜒))
3	1, 2	lb1d 57	1 ⊦ (𝜑 ⅋ (~ 𝜓 ⅋ 𝜒))

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-eac1 33

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

This theorem is referenced by:  dfli1i  65  dflb2s  92  licond  95