Theorem simp13 1056

Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)

Assertion

Ref	Expression
simp13	|- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ch )

Proof of Theorem simp13

Step	Hyp	Ref	Expression
1		simp3 1026	. 2 |- ( ( ph /\ ps /\ ch ) -> ch )
2	1	3ad2ant1 1045	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ch )

Syntax hints:   -> wi 4   /\ w3a 1005

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1007

This theorem is referenced by:  simpl13  1101  simpr13  1110  simp113  1155  simp213  1164  simp313  1173  funtpg  5388  dvdsgcd  12663  coprimeprodsq  12910  pythagtriplem4  12921  pythagtriplem13  12929  pythagtriplem14  12930  pythagtriplem16  12932  pythagtrip  12936