Theorem lbsymi 100

Description: Linear biconditional is symmetric. Inference for lbsym 127.

Hypothesis

Ref	Expression
lbsymi.1	⊦ (𝜑 ⧟ 𝜓)

Assertion

Ref	Expression
lbsymi	⊦ (𝜓 ⧟ 𝜑)

Proof of Theorem lbsymi

Step	Hyp	Ref	Expression
1		lbsymi.1	. 2 ⊦ (𝜑 ⧟ 𝜓)
2		lbrf 98	. 2 ⊦ (𝜑 ⧟ 𝜑)
3	1, 2	lbeui 99	1 ⊦ (𝜓 ⧟ 𝜑)

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:  lbtri  101