Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj930 Structured version   Unicode version

Theorem bnj930 32907
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj930.1  |-  ( ph  ->  F  Fn  A )
Assertion
Ref Expression
bnj930  |-  ( ph  ->  Fun  F )

Proof of Theorem bnj930
StepHypRef Expression
1 bnj930.1 . 2  |-  ( ph  ->  F  Fn  A )
2 fnfun 5676 . 2  |-  ( F  Fn  A  ->  Fun  F )
31, 2syl 16 1  |-  ( ph  ->  Fun  F )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   Fun wfun 5580    Fn wfn 5581
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 185  df-an 371  df-fn 5589
This theorem is referenced by:  bnj945  32911  bnj545  33032  bnj548  33034  bnj553  33035  bnj570  33042  bnj929  33073  bnj966  33081  bnj1442  33184  bnj1450  33185  bnj1501  33202
  Copyright terms: Public domain W3C validator