Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj835 Structured version   Visualization version   GIF version

Theorem bnj835 34773
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj835.1 (𝜂 ↔ (𝜑𝜓𝜒))
bnj835.2 (𝜑𝜏)
Assertion
Ref Expression
bnj835 (𝜂𝜏)

Proof of Theorem bnj835
StepHypRef Expression
1 bnj835.1 . 2 (𝜂 ↔ (𝜑𝜓𝜒))
2 bnj835.2 . . 3 (𝜑𝜏)
323ad2ant1 1134 . 2 ((𝜑𝜓𝜒) → 𝜏)
41, 3sylbi 217 1 (𝜂𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206  w3a 1087
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 207  df-an 396  df-3an 1089
This theorem is referenced by:  bnj1219  34814  bnj1379  34844  bnj1175  35018  bnj1286  35033  bnj1280  35034  bnj1296  35035  bnj1398  35048  bnj1415  35052  bnj1417  35055  bnj1421  35056  bnj1442  35063  bnj1450  35064  bnj1452  35066  bnj1489  35070  bnj1312  35072  bnj1501  35081  bnj1523  35085
  Copyright terms: Public domain W3C validator