Theorem aistia 43153

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 1545	. 2 ⊢ (𝜑 ↔ (𝜑 ↔ ⊤))
3	1, 2	mpbir 233	1 ⊢ 𝜑

Syntax hints:   ↔ wb 208  ⊤wtru 1538

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 209  df-tru 1540

This theorem is referenced by:  astbstanbst  43165  aistbistaandb  43166  aistbisfiaxb  43175  aisfbistiaxb  43176  aifftbifffaibif  43177  aifftbifffaibifff  43178  dandysum2p2e4  43254