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Theorem acasr 45
Description: & is associative. Reverse of acas 44.
Hypothesis
Ref Expression
acasr.1 (𝜑 ⅋ (𝜓 & (𝜒 & 𝜃)))
Assertion
Ref Expression
acasr (𝜑 ⅋ ((𝜓 & 𝜒) & 𝜃))

Proof of Theorem acasr
StepHypRef Expression
1 acasr.1 . . . 4 (𝜑 ⅋ (𝜓 & (𝜒 & 𝜃)))
21eac1d 37 . . 3 (𝜑𝜓)
31eac2d 39 . . . 4 (𝜑 ⅋ (𝜒 & 𝜃))
43eac1d 37 . . 3 (𝜑𝜒)
52, 4iac 35 . 2 (𝜑 ⅋ (𝜓 & 𝜒))
63eac2d 39 . 2 (𝜑𝜃)
75, 6iac 35 1 (𝜑 ⅋ ((𝜓 & 𝜒) & 𝜃))
Colors of variables: wff var nilad
Syntax hints:  wmd 2   & wac 30
This theorem was proved from axioms:  ax-ibot 4  ax-ebot 5  ax-cut 6  ax-init 7  ax-mdco 8  ax-iac 32  ax-eac1 33  ax-eac2 34
This theorem is referenced by: (None)
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