Theorem simp12l 1105

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

Assertion

Ref	Expression
simp12l	|- ( ( ( ch /\ ( ph /\ ps ) /\ th ) /\ ta /\ et ) -> ph )

Proof of Theorem simp12l

Step	Hyp	Ref	Expression
1		simp2l 1018	. 2 |- ( ( ch /\ ( ph /\ ps ) /\ th ) -> ph )
2	1	3ad2ant1 1013	1 |- ( ( ( ch /\ ( ph /\ ps ) /\ th ) /\ ta /\ et ) -> ph )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 973

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 975

This theorem is referenced by: (None)