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Theorem wl-3xorbi2 37475
Description: Alternative form of wl-3xorbi 37474. (Contributed by Mario Carneiro, 4-Sep-2016.) df-had redefined. (Revised by Wolf Lammen, 24-Apr-2024.)
Assertion
Ref Expression
wl-3xorbi2 (hadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑𝜓) ↔ 𝜒))

Proof of Theorem wl-3xorbi2
StepHypRef Expression
1 wl-3xorbi 37474 . 2 (hadd(𝜑, 𝜓, 𝜒) ↔ (𝜑 ↔ (𝜓𝜒)))
2 biass 384 . 2 (((𝜑𝜓) ↔ 𝜒) ↔ (𝜑 ↔ (𝜓𝜒)))
31, 2bitr4i 278 1 (hadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑𝜓) ↔ 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wb 206  haddwhad 1593
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 207  df-an 396  df-or 849  df-ifp 1064  df-xor 1512  df-tru 1543  df-had 1594
This theorem is referenced by:  wl-3xorbi123d  37476  wl-3xorrot  37478  wl-3xorcoma  37479  wl-3xornot  37482
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