Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1235 Structured version   Visualization version   GIF version

Theorem bnj1235 32080
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1235.1 (𝜑 ↔ (𝜓𝜒𝜃𝜏))
Assertion
Ref Expression
bnj1235 (𝜑𝜒)

Proof of Theorem bnj1235
StepHypRef Expression
1 bnj1235.1 . 2 (𝜑 ↔ (𝜓𝜒𝜃𝜏))
2 id 22 . 2 (𝜒𝜒)
31, 2bnj770 32038 1 (𝜑𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 208  w-bnj17 31960
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 209  df-an 399  df-3an 1085  df-bnj17 31961
This theorem is referenced by:  bnj966  32220  bnj967  32221  bnj910  32224  bnj1006  32236  bnj1018g  32239  bnj1018  32240  bnj1110  32258  bnj1121  32261  bnj1311  32300
  Copyright terms: Public domain W3C validator