Mathbox for Jarvin Udandy |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bothfbothsame | Structured version Visualization version GIF version |
Description: Given both a, b are equivalent to ⊥, there exists a proof for a is the same as b. (Contributed by Jarvin Udandy, 31-Aug-2016.) |
Ref | Expression |
---|---|
bothfbothsame.1 | ⊢ (𝜑 ↔ ⊥) |
bothfbothsame.2 | ⊢ (𝜓 ↔ ⊥) |
Ref | Expression |
---|---|
bothfbothsame | ⊢ (𝜑 ↔ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bothfbothsame.1 | . 2 ⊢ (𝜑 ↔ ⊥) | |
2 | bothfbothsame.2 | . 2 ⊢ (𝜓 ↔ ⊥) | |
3 | 1, 2 | bitr4i 266 | 1 ⊢ (𝜑 ↔ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 195 ⊥wfal 1480 |
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 196 |
This theorem is referenced by: mdandyv0 39765 mdandyv1 39766 mdandyv2 39767 mdandyv3 39768 mdandyv4 39769 mdandyv5 39770 mdandyv6 39771 mdandyv7 39772 mdandyv8 39773 mdandyv9 39774 mdandyv10 39775 mdandyv11 39776 mdandyv12 39777 mdandyv13 39778 mdandyv14 39779 dandysum2p2e4 39814 |
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