Users' Mathboxes 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 31096
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 1128 . . 3 ((𝜓𝜒𝜑) → 𝜓′)
3 bnj240.2 . . . 4 (𝜒𝜒′)
433ad2ant2 1129 . . 3 ((𝜓𝜒𝜑) → 𝜒′)
52, 4jca 555 . 2 ((𝜓𝜒𝜑) → (𝜓′𝜒′))
653comr 1120 1 ((𝜑𝜓𝜒) → (𝜓′𝜒′))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  w3a 1072
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
This theorem is referenced by:  bnj594  31311  bnj580  31312  bnj966  31343  bnj967  31344
  Copyright terms: Public domain W3C validator