Theorem 3adantl3 1122

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
3adantl3	|- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )

Proof of Theorem 3adantl3

Step	Hyp	Ref	Expression
1		3simpa 961	. 2 |- ( ( ph /\ ps /\ ta ) -> ( ph /\ ps ) )
2		3adantl.1	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	1, 2	sylan 279	1 |- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 945

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

This theorem depends on definitions:  df-bi 116  df-3an 947

This theorem is referenced by:  ltsopr  7352  lediv2a  8563  muldvds1  11366  muldvds2  11367  dvdscmul  11368  dvdsmulc  11369  rpexp  11677  iscnp4  12229  cnpnei  12230  xblm  12406