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Theorem embantd 55
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 53 . 2 (𝜑 → ((𝜓𝜒) → (𝜓𝜃)))
41, 3mpid 41 1 (𝜑 → ((𝜓𝜒) → 𝜃))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  a2and  525  el  4005  findcard2d  6587  findcard2sd  6588  exprmfct  11212  sqrt2irr  11234  bj-exlimmp  11327
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