Mathbox for Jarvin Udandy |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > aisbbisfaisf | Structured version Visualization version GIF version |
Description: Given a is equivalent to b, b is equivalent to ⊥ there exists a proof for a is equivalent to F. (Contributed by Jarvin Udandy, 30-Aug-2016.) |
Ref | Expression |
---|---|
aisbbisfaisf.1 | ⊢ (𝜑 ↔ 𝜓) |
aisbbisfaisf.2 | ⊢ (𝜓 ↔ ⊥) |
Ref | Expression |
---|---|
aisbbisfaisf | ⊢ (𝜑 ↔ ⊥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | aisbbisfaisf.1 | . 2 ⊢ (𝜑 ↔ 𝜓) | |
2 | aisbbisfaisf.2 | . 2 ⊢ (𝜓 ↔ ⊥) | |
3 | 1, 2 | bitri 278 | 1 ⊢ (𝜑 ↔ ⊥) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 209 ⊥wfal 1554 |
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 |
This theorem is referenced by: mdandysum2p2e4 44033 |
Copyright terms: Public domain | W3C validator |