Theorem id 77

Description: Identity rule for linear implication. Syllogism form of ax-init 7.

Assertion

Ref	Expression
id	⊦ (𝜑 ⊸ 𝜑)

Proof of Theorem id

Step	Hyp	Ref	Expression
1		ax-init 7	. 2 ⊦ (~ 𝜑 ⅋ 𝜑)
2		df-li 62	. 2 ⊦ ((𝜑 ⊸ 𝜑) ⧟ (~ 𝜑 ⅋ 𝜑))
3	1, 2	lb2i 60	1 ⊦ (𝜑 ⊸ 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-eac1 33  ax-eac2 34

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

This theorem is referenced by:  licon  94  lbrf  98  mcco  115