Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > simpr3r | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simpr3r | ⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp3r 1083 | . 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜓) | |
2 | 1 | adantl 481 | 1 ⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∧ w3a 1031 |
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 df-3an 1033 |
This theorem is referenced by: ax5seg 25618 segconeq 31287 ifscgr 31321 btwnconn1lem9 31372 btwnconn1lem11 31374 btwnconn1lem12 31375 lplnexllnN 33868 cdleme3b 34534 cdleme3c 34535 cdleme3e 34537 cdleme27a 34673 |
Copyright terms: Public domain | W3C validator |