Theorem 3adantl2 1180

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 1021	. 2 |- ( ( ph /\ ta /\ ps ) -> ( ph /\ ps ) )
2		3adantl.1	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	1, 2	sylan 283	1 |- ( ( ( ph /\ ta /\ ps ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1004

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 1006

This theorem is referenced by:  3ad2antl1  1185  nnmord  6685  ltaprg  7839  lediv2a  9075  zdiv  9568  mulgnn0subcl  13740  mulgsubcl  13741  ghmmulg  13861  neiint  14888  cnpnei  14962  clwwlkext2edg  16292