MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ad5antlr Structured version   Unicode version

Theorem ad5antlr 734
Description: Deduction adding 5 conjuncts to antecedent. (Contributed by Mario Carneiro, 5-Jan-2017.)
Hypothesis
Ref Expression
ad2ant.1  |-  ( ph  ->  ps )
Assertion
Ref Expression
ad5antlr  |-  ( ( ( ( ( ( ch  /\  ph )  /\  th )  /\  ta )  /\  et )  /\  ze )  ->  ps )

Proof of Theorem ad5antlr
StepHypRef Expression
1 ad2ant.1 . . 3  |-  ( ph  ->  ps )
21ad4antlr 732 . 2  |-  ( ( ( ( ( ch 
/\  ph )  /\  th )  /\  ta )  /\  et )  ->  ps )
32adantr 465 1  |-  ( ( ( ( ( ( ch  /\  ph )  /\  th )  /\  ta )  /\  et )  /\  ze )  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
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
This theorem is referenced by:  ad6antlr  736  restmetu  20162  pstmxmet  26324  mblfinlem3  28430  itg2gt0cn  28447  pell1234qrmulcl  29196  usg2spot2nb  30658
  Copyright terms: Public domain W3C validator