NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  hadbi123i GIF version

Theorem hadbi123i 1384
Description: Equality theorem for half adder. (Contributed by Mario Carneiro, 4-Sep-2016.)
Hypotheses
Ref Expression
hadbii.1 (φψ)
hadbii.2 (χθ)
hadbii.3 (τη)
Assertion
Ref Expression
hadbi123i (hadd(φ, χ, τ) ↔ hadd(ψ, θ, η))

Proof of Theorem hadbi123i
StepHypRef Expression
1 hadbii.1 . . . 4 (φψ)
21a1i 10 . . 3 ( ⊤ → (φψ))
3 hadbii.2 . . . 4 (χθ)
43a1i 10 . . 3 ( ⊤ → (χθ))
5 hadbii.3 . . . 4 (τη)
65a1i 10 . . 3 ( ⊤ → (τη))
72, 4, 6hadbi123d 1382 . 2 ( ⊤ → (hadd(φ, χ, τ) ↔ hadd(ψ, θ, η)))
87trud 1323 1 (hadd(φ, χ, τ) ↔ hadd(ψ, θ, η))
Colors of variables: wff setvar class
Syntax hints:  wb 176  wtru 1316  haddwhad 1378
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-xor 1305  df-tru 1319  df-had 1380
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator