Mathbox for Jarvin Udandy |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > aistia | Structured version Visualization version GIF version |
Description: Given a is equivalent to ⊤, there exists a proof for a. (Contributed by Jarvin Udandy, 30-Aug-2016.) |
Ref | Expression |
---|---|
aistia.1 | ⊢ (𝜑 ↔ ⊤) |
Ref | Expression |
---|---|
aistia | ⊢ 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | aistia.1 | . 2 ⊢ (𝜑 ↔ ⊤) | |
2 | tbtru 1550 | . 2 ⊢ (𝜑 ↔ (𝜑 ↔ ⊤)) | |
3 | 1, 2 | mpbir 234 | 1 ⊢ 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 209 ⊤wtru 1543 |
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 210 df-tru 1545 |
This theorem is referenced by: astbstanbst 43943 aistbistaandb 43944 aistbisfiaxb 43953 aisfbistiaxb 43954 aifftbifffaibif 43955 aifftbifffaibifff 43956 dandysum2p2e4 44032 |
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