MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  alanimi Structured version   Unicode version

Theorem alanimi 1608
Description: Variant of al2imi 1607 with conjunctive antecedent. (Contributed by Andrew Salmon, 8-Jun-2011.)
Hypothesis
Ref Expression
alanimi.1  |-  ( (
ph  /\  ps )  ->  ch )
Assertion
Ref Expression
alanimi  |-  ( ( A. x ph  /\  A. x ps )  ->  A. x ch )

Proof of Theorem alanimi
StepHypRef Expression
1 alanimi.1 . . . 4  |-  ( (
ph  /\  ps )  ->  ch )
21ex 434 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
32al2imi 1607 . 2  |-  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) )
43imp 429 1  |-  ( ( A. x ph  /\  A. x ps )  ->  A. x ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369   A.wal 1368
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  19.26  1648  alsyl  1670  nfeqf  2005  bm1.1  2437  vtoclgft  3126  euind  3253  reuind  3270  sbeqalb  3351  bm1.3ii  4527  trin2  5332  mpt2bi123f  29143  mptbi12f  29147  albitr  29783  2alanimi  29792  bj-cbv3ta  32558
  Copyright terms: Public domain W3C validator