Theorem lbtri 101

Description: Linear biconditional is transitive. Inference for lbtr 128.

Hypotheses

Ref	Expression
lbtri.1	⊦ (𝜑 ⧟ 𝜓)
lbtri.2	⊦ (𝜓 ⧟ 𝜒)

Assertion

Ref	Expression
lbtri	⊦ (𝜑 ⧟ 𝜒)

Proof of Theorem lbtri

Step	Hyp	Ref	Expression
1		lbtri.1	. . 3 ⊦ (𝜑 ⧟ 𝜓)
2	1	lbsymi 100	. 2 ⊦ (𝜓 ⧟ 𝜑)
3		lbtri.2	. 2 ⊦ (𝜓 ⧟ 𝜒)
4	2, 3	lbeui 99	1 ⊦ (𝜑 ⧟ 𝜒)

Syntax hints:   ⧟ wlb 55

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-iac 32  ax-eac1 33  ax-eac2 34

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

This theorem is referenced by: (None)