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Theorem wl-df3xor3 36351
Description: Alternative form of wl-df3xor2 36350. Copy of df-had 1596. (Contributed by Mario Carneiro, 4-Sep-2016.) df-had redefined. (Revised by Wolf Lammen, 1-May-2024.)
Assertion
Ref Expression
wl-df3xor3 (hadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑𝜓) ⊻ 𝜒))

Proof of Theorem wl-df3xor3
StepHypRef Expression
1 wl-df3xor2 36350 . 2 (hadd(𝜑, 𝜓, 𝜒) ↔ (𝜑 ⊻ (𝜓𝜒)))
2 xorass 1515 . 2 (((𝜑𝜓) ⊻ 𝜒) ↔ (𝜑 ⊻ (𝜓𝜒)))
31, 2bitr4i 278 1 (hadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑𝜓) ⊻ 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wb 205  wxo 1510  haddwhad 1595
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 206  df-an 398  df-or 847  df-ifp 1063  df-xor 1511  df-tru 1545  df-had 1596
This theorem is referenced by: (None)
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