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Theorem anass1rs 505
Description: Commutative-associative law for conjunction in an antecedent. (Contributed by Jeff Madsen, 19-Jun-2011.)
Hypothesis
Ref Expression
anass1rs.1 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
Assertion
Ref Expression
anass1rs (((𝜑𝜒) ∧ 𝜓) → 𝜃)

Proof of Theorem anass1rs
StepHypRef Expression
1 anass1rs.1 . . 3 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
21anassrs 380 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
32an32s 502 1 (((𝜑𝜒) ∧ 𝜓) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  creui  7888  qreccl  8547
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