Theorem 3adantl1 1060

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)

Hypothesis

Ref	Expression
3adantl.1	|- ( ( ( ph /\ ps ) /\ ch ) -> th )

Assertion

Ref	Expression
3adantl1	|- ( ( ( ta /\ ph /\ ps ) /\ ch ) -> th )

Proof of Theorem 3adantl1

Step	Hyp	Ref	Expression
1		3simpc 903	. 2 |- ( ( ta /\ ph /\ ps ) -> ( ph /\ ps ) )
2		3adantl.1	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	1, 2	sylan 267	1 |- ( ( ( ta /\ ph /\ ps ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 97   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  3ad2antl2  1067  3ad2antl3  1068  distrlem1prl  6680  distrlem1pru  6681  divmuldivap  7688  expnlbnd  9373