Theorem aistia 47694

Description: Given a is equivalent to ⊤, there exists a proof for a. (Contributed by Jarvin Udandy, 30-Aug-2016.)

Hypothesis

Ref	Expression
aistia.1	⊢ (𝜑 ↔ ⊤)

Assertion

Ref	Expression
aistia	⊢ 𝜑

Proof of Theorem aistia

Step	Hyp	Ref	Expression
1		aistia.1	. 2 ⊢ (𝜑 ↔ ⊤)
2		tbtru 1578	. 2 ⊢ (𝜑 ↔ (𝜑 ↔ ⊤))
3	1, 2	mpbir 234	1 ⊢ 𝜑

This proof depends on syntax axioms:   ↔ wb 209  ⊤wtru 1571

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-tru 1573

This theorem is used by:  astbstanbst  47706  aistbistaandb  47707  aistbisfiaxb  47716  aisfbistiaxb  47717  aifftbifffaibif  47718  aifftbifffaibifff  47719  dandysum2p2e4  47795