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Theorem embantd 56
Description: Deduction embedding an antecedent. (Contributed by Wolf Lammen, 4-Oct-2013.)
Hypotheses
Ref Expression
embantd.1 (𝜑𝜓)
embantd.2 (𝜑 → (𝜒𝜃))
Assertion
Ref Expression
embantd (𝜑 → ((𝜓𝜒) → 𝜃))

Proof of Theorem embantd
StepHypRef Expression
1 embantd.1 . 2 (𝜑𝜓)
2 embantd.2 . . 3 (𝜑 → (𝜒𝜃))
32imim2d 54 . 2 (𝜑 → ((𝜓𝜒) → (𝜓𝜃)))
41, 3mpid 42 1 (𝜑 → ((𝜓𝜒) → 𝜃))
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  11829  sqrt2irr  11851  iscnp4  12401  bj-exlimmp  13035
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