Theorem 3ad2antl2 809

Description: Deduction adding conjuncts to antecedent.

Hypothesis

Ref	Expression
3ad2antl.1	|- ((ph /\ ch) -> th)

Assertion

Ref	Expression
3ad2antl2	|- (((ps /\ ph /\ ta) /\ ch) -> th)

Proof of Theorem 3ad2antl2

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 |- ((ph /\ ch) -> th)
2	1	adantlr 393	. 2 |- (((ph /\ ta) /\ ch) -> th)
3	2	3adantl1 802	1 |- (((ps /\ ph /\ ta) /\ ch) -> th)

Syntax hints:   -> wi 3   /\ wa 223   /\ w3a 774

This theorem is referenced by:  divdiv23t 5762  dnsconst 7767  ssblex 7839  cncfmet 7888  nvmul0or 8257  lnoadd 8405  lnosub 8406  hoadddit 9720  idmon 10695

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225  df-3an 776

Copyright terms: Public domain