Mathbox for Jarvin Udandy |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > mdandyvr11 | Structured version Visualization version GIF version |
Description: Given the equivalences set in the hypotheses, there exist a proof where ch, th, ta, et match ze, si accordingly. (Contributed by Jarvin Udandy, 7-Sep-2016.) |
Ref | Expression |
---|---|
mdandyvr11.1 | ⊢ (𝜑 ↔ 𝜁) |
mdandyvr11.2 | ⊢ (𝜓 ↔ 𝜎) |
mdandyvr11.3 | ⊢ (𝜒 ↔ 𝜓) |
mdandyvr11.4 | ⊢ (𝜃 ↔ 𝜓) |
mdandyvr11.5 | ⊢ (𝜏 ↔ 𝜑) |
mdandyvr11.6 | ⊢ (𝜂 ↔ 𝜓) |
Ref | Expression |
---|---|
mdandyvr11 | ⊢ ((((𝜒 ↔ 𝜎) ∧ (𝜃 ↔ 𝜎)) ∧ (𝜏 ↔ 𝜁)) ∧ (𝜂 ↔ 𝜎)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mdandyvr11.2 | . 2 ⊢ (𝜓 ↔ 𝜎) | |
2 | mdandyvr11.1 | . 2 ⊢ (𝜑 ↔ 𝜁) | |
3 | mdandyvr11.3 | . 2 ⊢ (𝜒 ↔ 𝜓) | |
4 | mdandyvr11.4 | . 2 ⊢ (𝜃 ↔ 𝜓) | |
5 | mdandyvr11.5 | . 2 ⊢ (𝜏 ↔ 𝜑) | |
6 | mdandyvr11.6 | . 2 ⊢ (𝜂 ↔ 𝜓) | |
7 | 1, 2, 3, 4, 5, 6 | mdandyvr4 39785 | 1 ⊢ ((((𝜒 ↔ 𝜎) ∧ (𝜃 ↔ 𝜎)) ∧ (𝜏 ↔ 𝜁)) ∧ (𝜂 ↔ 𝜎)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 195 ∧ wa 383 |
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 df-an 385 |
This theorem is referenced by: (None) |
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