MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  3adant1l Structured version   Unicode version

Theorem 3adant1l 1176
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
Hypothesis
Ref Expression
3adant1l.1  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
3adant1l  |-  ( ( ( ta  /\  ph )  /\  ps  /\  ch )  ->  th )

Proof of Theorem 3adant1l
StepHypRef Expression
1 3adant1l.1 . . . 4  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213expb 1154 . . 3  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
32adantll 695 . 2  |-  ( ( ( ta  /\  ph )  /\  ( ps  /\  ch ) )  ->  th )
433impb 1149 1  |-  ( ( ( ta  /\  ph )  /\  ps  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359    /\ w3a 936
This theorem is referenced by:  3adant2l  1178  3adant3l  1180  cfsmolem  8140  axdc3lem4  8323  spwpr4  14653  issubmnd  14714  restnlly  17535  hasheuni  24465  pellex  26852  mendlmod  27433
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 178  df-an 361  df-3an 938
  Copyright terms: Public domain W3C validator