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Theorem embantd 56
Description: Deduction embedding an antecedent. (Contributed by Wolf Lammen, 4-Oct-2013.)
Hypotheses
Ref Expression
embantd.1  |-  ( ph  ->  ps )
embantd.2  |-  ( ph  ->  ( ch  ->  th )
)
Assertion
Ref Expression
embantd  |-  ( ph  ->  ( ( ps  ->  ch )  ->  th )
)

Proof of Theorem embantd
StepHypRef Expression
1 embantd.1 . 2  |-  ( ph  ->  ps )
2 embantd.2 . . 3  |-  ( ph  ->  ( ch  ->  th )
)
32imim2d 54 . 2  |-  ( ph  ->  ( ( ps  ->  ch )  ->  ( ps  ->  th ) ) )
41, 3mpid 42 1  |-  ( ph  ->  ( ( ps  ->  ch )  ->  th )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  a2and  547  el  4102  findcard2d  6785  findcard2sd  6786  exprmfct  11825  sqrt2irr  11847  iscnp4  12397  bj-exlimmp  12990
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