Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > simpr2r | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simpr2r | ⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp2r 1081 | . 2 ⊢ ((𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃) → 𝜓) | |
2 | 1 | adantl 481 | 1 ⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 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: oppccatid 16202 subccatid 16329 setccatid 16557 catccatid 16575 estrccatid 16595 xpccatid 16651 gsmsymgreqlem1 17673 kerf1hrm 18566 ax5seg 25618 segconeq 31287 ifscgr 31321 brofs2 31354 brifs2 31355 idinside 31361 btwnconn1lem8 31371 btwnconn1lem11 31374 btwnconn1lem12 31375 segcon2 31382 seglecgr12im 31387 unbdqndv2 31672 lplnexllnN 33868 paddasslem9 34132 paddasslem15 34138 pmodlem2 34151 lhp2lt 34305 3pthdlem1 41331 |
Copyright terms: Public domain | W3C validator |