Theorem 3adantl1 1155

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 998	. 2 |- ( ( ta /\ ph /\ ps ) -> ( ph /\ ps ) )
2		3adantl.1	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	1, 2	sylan 283	1 |- ( ( ( ta /\ ph /\ ps ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 980

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 982

This theorem is referenced by:  3ad2antl2  1162  3ad2antl3  1163  distrlem1prl  7666  distrlem1pru  7667  divmuldivap  8756  modqaddmulmod  10500  expnlbnd  10773  lcmledvds  12263  ctinf  12672  upxp  14592