Mathbox for Jarvin Udandy |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > abcdta | Structured version Visualization version GIF version |
Description: Given (((a and b) and c) and d), there exists a proof for a. (Contributed by Jarvin Udandy, 3-Sep-2016.) |
Ref | Expression |
---|---|
abcdta.1 | ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) |
Ref | Expression |
---|---|
abcdta | ⊢ 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | abcdta.1 | . . . 4 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) | |
2 | 1 | simpli 487 | . . 3 ⊢ ((𝜑 ∧ 𝜓) ∧ 𝜒) |
3 | 2 | simpli 487 | . 2 ⊢ (𝜑 ∧ 𝜓) |
4 | 3 | simpli 487 | 1 ⊢ 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 399 |
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-an 400 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |