Theorem 3adantl3 1186

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 1025	. 2 |- ( ( ph /\ ps /\ ta ) -> ( ph /\ ps ) )
2		3adantl.1	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	1, 2	sylan 283	1 |- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  ltsopr  7963  lediv2a  9225  nn0p1elfzo  10594  muldvds1  12583  muldvds2  12584  dvdscmul  12585  dvdsmulc  12586  rpexp  12931  iscnp4  15319  cnpnei  15320  xblm  15518