Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj240 Structured version   Visualization version   GIF version

Theorem bnj240 31987
 Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj240.1 (𝜓𝜓′)
bnj240.2 (𝜒𝜒′)
Assertion
Ref Expression
bnj240 ((𝜑𝜓𝜒) → (𝜓′𝜒′))

Proof of Theorem bnj240
StepHypRef Expression
1 bnj240.1 . . . 4 (𝜓𝜓′)
213ad2ant1 1130 . . 3 ((𝜓𝜒𝜑) → 𝜓′)
3 bnj240.2 . . . 4 (𝜒𝜒′)
433ad2ant2 1131 . . 3 ((𝜓𝜒𝜑) → 𝜒′)
52, 4jca 515 . 2 ((𝜓𝜒𝜑) → (𝜓′𝜒′))
653comr 1122 1 ((𝜑𝜓𝜒) → (𝜓′𝜒′))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1084 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  df-3an 1086 This theorem is referenced by:  bnj594  32202  bnj580  32203  bnj966  32234  bnj967  32235
 Copyright terms: Public domain W3C validator