Theorem simp13 1060

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 1030	. 2 |- ( ( ph /\ ps /\ ch ) -> ch )
2	1	3ad2ant1 1049	1 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ch )

This proof depends on syntax axioms:   -> wi 4   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  simpl13  1105  simpr13  1114  simp113  1159  simp213  1168  simp313  1177  funtpg  5432  dvdsgcd  12789  coprimeprodsq  13036  pythagtriplem4  13047  pythagtriplem13  13055  pythagtriplem14  13056  pythagtriplem16  13058  pythagtrip  13062