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Theorem 3ad2antr2 1105
Description: Deduction adding a conjuncts to antecedent. (Contributed by NM, 27-Dec-2007.)
Hypothesis
Ref Expression
3ad2antl.1  |-  ( (
ph  /\  ch )  ->  th )
Assertion
Ref Expression
3ad2antr2  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  ta )
)  ->  th )

Proof of Theorem 3ad2antr2
StepHypRef Expression
1 3ad2antl.1 . . 3  |-  ( (
ph  /\  ch )  ->  th )
21adantrl 462 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
323adantr3 1100 1  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  ta )
)  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    /\ w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  prarloclem  6753  ioc0  9349
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