Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e01an Unicode version

Theorem e01an 28465
Description: Conjunction form of e01 28463. (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e01an.1  |-  ph
e01an.2  |-  (. ps  ->.  ch
).
e01an.3  |-  ( (
ph  /\  ch )  ->  th )
Assertion
Ref Expression
e01an  |-  (. ps  ->.  th
).

Proof of Theorem e01an
StepHypRef Expression
1 e01an.1 . 2  |-  ph
2 e01an.2 . 2  |-  (. ps  ->.  ch
).
3 e01an.3 . . 3  |-  ( (
ph  /\  ch )  ->  th )
43ex 423 . 2  |-  ( ph  ->  ( ch  ->  th )
)
51, 2, 4e01 28463 1  |-  (. ps  ->.  th
).
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   (.wvd1 28337
This theorem is referenced by:  unipwrVD  28608
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-vd1 28338
  Copyright terms: Public domain W3C validator