ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3adant3r Unicode version

Theorem 3adant3r 1181
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
3adant3r  |-  ( (
ph  /\  ps  /\  ( ch  /\  ta ) )  ->  th )

Proof of Theorem 3adant3r
StepHypRef Expression
1 3adant1l.1 . . . 4  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213com13 1154 . . 3  |-  ( ( ch  /\  ps  /\  ph )  ->  th )
323adant1r 1177 . 2  |-  ( ( ( ch  /\  ta )  /\  ps  /\  ph )  ->  th )
433com13 1154 1  |-  ( (
ph  /\  ps  /\  ( ch  /\  ta ) )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 930
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 932
This theorem is referenced by:  addassnqg  7091  mulassnqg  7093  prarloc  7212  ltpopr  7304  ltexprlemfl  7318  ltexprlemfu  7320  addasssrg  7452  axaddass  7557  apmul1  8409  ltmul2  8472  lemul2  8473  dvdscmulr  11317  dvdsmulcr  11318  modremain  11421  ndvdsadd  11423  rpexp12i  11626  xblcntrps  12341  xblcntr  12342
  Copyright terms: Public domain W3C validator