Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1232 Structured version   Visualization version   GIF version

Theorem bnj1232 31391
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1232.1 (𝜑 ↔ (𝜓𝜒𝜃𝜏))
Assertion
Ref Expression
bnj1232 (𝜑𝜓)

Proof of Theorem bnj1232
StepHypRef Expression
1 bnj1232.1 . 2 (𝜑 ↔ (𝜓𝜒𝜃𝜏))
2 bnj642 31335 . 2 ((𝜓𝜒𝜃𝜏) → 𝜓)
31, 2sylbi 209 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 198  w-bnj17 31272
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 199  df-an 386  df-3an 1110  df-bnj17 31273
This theorem is referenced by:  bnj605  31494  bnj607  31503  bnj944  31525  bnj969  31533  bnj970  31534  bnj1001  31545  bnj1110  31567  bnj1118  31569  bnj1128  31575  bnj1145  31578  bnj1311  31609
  Copyright terms: Public domain W3C validator