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Theorem 3ad2antr3 1133
Description: Deduction adding a conjuncts to antecedent. (Contributed by NM, 30-Dec-2007.)
Hypothesis
Ref Expression
3ad2antl.1  |-  ( (
ph  /\  ch )  ->  th )
Assertion
Ref Expression
3ad2antr3  |-  ( (
ph  /\  ( ps  /\ 
ta  /\  ch )
)  ->  th )

Proof of Theorem 3ad2antr3
StepHypRef Expression
1 3ad2antl.1 . . 3  |-  ( (
ph  /\  ch )  ->  th )
21adantrl 469 . 2  |-  ( (
ph  /\  ( ta  /\ 
ch ) )  ->  th )
323adantr1 1125 1  |-  ( (
ph  /\  ( ps  /\ 
ta  /\  ch )
)  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 947
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 949
This theorem is referenced by:  ordwe  4460
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