Theorem 3adantl3 1150

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 989	. 2 |- ( ( ph /\ ps /\ ta ) -> ( ph /\ ps ) )
2		3adantl.1	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	1, 2	sylan 281	1 |- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )

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:  ltsopr  7558  lediv2a  8811  muldvds1  11778  muldvds2  11779  dvdscmul  11780  dvdsmulc  11781  rpexp  12107  iscnp4  13012  cnpnei  13013  xblm  13211