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Theorem mpidan 414
Description: A deduction which "stacks" a hypothesis. (Contributed by Stanislas Polu, 9-Mar-2020.) (Proof shortened by Wolf Lammen, 28-Mar-2021.)
Hypotheses
Ref Expression
mpidan.1  |-  ( ph  ->  ch )
mpidan.2  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
Assertion
Ref Expression
mpidan  |-  ( (
ph  /\  ps )  ->  th )

Proof of Theorem mpidan
StepHypRef Expression
1 mpidan.1 . . 3  |-  ( ph  ->  ch )
21adantr 270 . 2  |-  ( (
ph  /\  ps )  ->  ch )
3 mpidan.2 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
42, 3mpdan 412 1  |-  ( (
ph  /\  ps )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
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 is referenced by:  isumrb  10402
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