Theorem simpl13 1064

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simpl13	|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et ) -> ch )

Proof of Theorem simpl13

Step	Hyp	Ref	Expression
1		simp13 1019	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ch )
2	1	adantr 274	1 |- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et ) -> ch )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 968

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 970

This theorem is referenced by:  pythagtriplem4  12200