Substitutivity of Equivalence= sub 1.}y (M=N)(=AN) 2. FhM=N. then a= am 3.fHM≡Nand+A, then a Theorems 1.+x(A≡B)(A≡wB) 2.m(A≡B)(丑mA≡3xB) Logic in Computer Science - p 7/27Substitutivity of Equivalence≡ Sub 1. ` ∀y1 · · · yk(M ≡ N) ⊃ (A ≡ AMN ) 2. If ` M ≡ N, then ` A ≡ AMN 3. If ` M ≡ N and ` A, then ` AMN Theorems 1. ` ∀x(A ≡ B) ⊃ (∀xA ≡ ∀xB) 2. ` ∀x(A ≡ B) ⊃ (∃xA ≡ ∃xB) Logic in Computer Science – p.7/27