Mathbox for Jarvin Udandy |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > aiffbtbat | Structured version Visualization version GIF version |
Description: Given a is equivalent to b, T. is equivalent to b. there exists a proof for a is equivalent to T. (Contributed by Jarvin Udandy, 29-Aug-2016.) |
Ref | Expression |
---|---|
aiffbtbat.1 | ⊢ (𝜑 ↔ 𝜓) |
aiffbtbat.2 | ⊢ (⊤ ↔ 𝜓) |
Ref | Expression |
---|---|
aiffbtbat | ⊢ (𝜑 ↔ ⊤) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | aiffbtbat.1 | . 2 ⊢ (𝜑 ↔ 𝜓) | |
2 | aiffbtbat.2 | . 2 ⊢ (⊤ ↔ 𝜓) | |
3 | 1, 2 | bitr4i 281 | 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 |
This theorem is referenced by: (None) |
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