Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > hypstkdOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of mpidan 701 as of 28-Mar-2021. (Contributed by Stanislas Polu, 9-Mar-2020.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
hypstkdOLD.1 | ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
hypstkdOLD.2 | ⊢ (𝜑 → 𝜒) |
Ref | Expression |
---|---|
hypstkdOLD | ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . 2 ⊢ ((𝜑 ∧ 𝜓) → (𝜑 ∧ 𝜓)) | |
2 | hypstkdOLD.2 | . . 3 ⊢ (𝜑 → 𝜒) | |
3 | 2 | adantr 480 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
4 | hypstkdOLD.1 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) | |
5 | 1, 3, 4 | syl2anc 691 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ 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) |
Copyright terms: Public domain | W3C validator |