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Theorem wl-embant 32964
Description: A true wff can always be added as a nested antecedent to an antecedent. Note: this theorem is intuitionistically valid. (Contributed by Wolf Lammen, 4-Oct-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
wl-embant.1 𝜑
wl-embant.2 (𝜓𝜒)
Assertion
Ref Expression
wl-embant ((𝜑𝜓) → 𝜒)

Proof of Theorem wl-embant
StepHypRef Expression
1 wl-embant.1 . 2 𝜑
2 wl-embant.2 . . 3 (𝜓𝜒)
32imim2i 16 . 2 ((𝜑𝜓) → (𝜑𝜒))
41, 3mpi 20 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar 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: (None)
  Copyright terms: Public domain W3C validator