Theorem 3adantl2 1144

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
3adantl2	|- ( ( ( ph /\ ta /\ ps ) /\ ch ) -> th )

Proof of Theorem 3adantl2

Step	Hyp	Ref	Expression
1		3simpb 985	. 2 |- ( ( ph /\ ta /\ ps ) -> ( ph /\ ps ) )
2		3adantl.1	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	1, 2	sylan 281	1 |- ( ( ( ph /\ ta /\ ps ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 968

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 970

This theorem is referenced by:  3ad2antl1  1149  nnmord  6485  ltaprg  7560  lediv2a  8790  zdiv  9279  neiint  12785  cnpnei  12859