Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj707 Structured version   Visualization version   GIF version

Theorem bnj707 31153
 Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj707.1 (𝜒𝜏)
Assertion
Ref Expression
bnj707 ((𝜑𝜓𝜒𝜃) → 𝜏)

Proof of Theorem bnj707
StepHypRef Expression
1 bnj258 31104 . . 3 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓𝜃) ∧ 𝜒))
21simprbi 483 . 2 ((𝜑𝜓𝜒𝜃) → 𝜒)
3 bnj707.1 . 2 (𝜒𝜏)
42, 3syl 17 1 ((𝜑𝜓𝜒𝜃) → 𝜏)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 1072   ∧ w-bnj17 31082 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 197  df-an 385  df-3an 1074  df-bnj17 31083 This theorem is referenced by:  bnj771  31162  bnj998  31354  bnj1001  31356  bnj1006  31357  bnj1053  31372  bnj1121  31381  bnj1030  31383
 Copyright terms: Public domain W3C validator