Theorem lbi1 89

Description: Extract forward implication from biconditional. Alternate form of lb1i 59.

Hypothesis

Ref	Expression
lbi1.1	⊦ (𝜑 ⧟ 𝜓)

Assertion

Ref	Expression
lbi1	⊦ (𝜑 ⊸ 𝜓)

Proof of Theorem lbi1

Step	Hyp	Ref	Expression
1		lbi1.1	. 2 ⊦ (𝜑 ⧟ 𝜓)
2		lbi1s 87	. 2 ⊦ ((𝜑 ⧟ 𝜓) ⊸ (𝜑 ⊸ 𝜓))
3	1, 2	lmp 76	1 ⊦ (𝜑 ⊸ 𝜓)

Syntax hints:   ⧟ wlb 55   ⊸ wli 61

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-eac1 33  ax-eac2 34

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

This theorem is referenced by:  lbeui  99  md2  114  abs1  178