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∧Intro

∧Elim₁ and ∧Elim₂

∨Intro₁ and ∨Intro₂

∨Elim

→ Intro

→ Elim

¬Intro

¬Elim

↔Intro

↔Elim₁ and ↔Elim₂

∀Elim

∃Intro

∀Intro
Provided the constant t does not occur in φ or in any undischarged assumption in the proof of φ[t/v].
![<p>Provided the constant t does not occur in φ or in any undischarged assumption in the proof of φ[t/v].</p>](https://knowt-user-attachments.s3.amazonaws.com/827d43df-811b-48fe-b0c6-0d4fed1fc46f.jpg)
∃Elim
provided that the constant t does not occur in ∃vφ or in ψ or in any undischarged assumption other than φ[t/v] in the proof of ψ.
![<p>provided that the constant t does not occur in ∃vφ or in ψ or in any undischarged assumption other than φ[t/v] in the proof of ψ.</p>](https://knowt-user-attachments.s3.amazonaws.com/98edd8a6-ad35-461a-b307-0cec308ba8ee.jpg)
=Intro

=Elim
