Theorem aistia 46867

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 1547	. 2 ⊢ (𝜑 ↔ (𝜑 ↔ ⊤))
3	1, 2	mpbir 231	1 ⊢ 𝜑

Syntax hints:   ↔ wb 206  ⊤wtru 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-tru 1542

This theorem is referenced by:  astbstanbst  46879  aistbistaandb  46880  aistbisfiaxb  46889  aisfbistiaxb  46890  aifftbifffaibif  46891  aifftbifffaibifff  46892  dandysum2p2e4  46968