MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ancom1s Structured version   Unicode version

Theorem ancom1s 781
Description: Inference commuting a nested conjunction in antecedent. (Contributed by NM, 24-May-2006.) (Proof shortened by Wolf Lammen, 24-Nov-2012.)
Hypothesis
Ref Expression
an32s.1  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
Assertion
Ref Expression
ancom1s  |-  ( ( ( ps  /\  ph )  /\  ch )  ->  th )

Proof of Theorem ancom1s
StepHypRef Expression
1 pm3.22 437 . 2  |-  ( ( ps  /\  ph )  ->  ( ph  /\  ps ) )
2 an32s.1 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
31, 2sylan 458 1  |-  ( ( ( ps  /\  ph )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359
This theorem is referenced by:  odi  6814  sornom  8147  leltadd  9502  divmul13  9707  absmax  12123  fzomaxdif  12137  iocopnst  18955  mumul  20954  lgsdir2  21102  branmfn  23598  chirredlem2  23884  chirredlem4  23886  comppfsc  26341  frinfm  26391  fzmul  26398  fdc  26403  rpnnen3  27057  unxpwdom3  27188
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
  Copyright terms: Public domain W3C validator