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Theorem 3an1rs 1453
Description: Swap conjuncts. (Contributed by NM, 16-Dec-2007.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)
Hypothesis
Ref Expression
3an1rs.1 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
Assertion
Ref Expression
3an1rs (((𝜑𝜓𝜃) ∧ 𝜒) → 𝜏)

Proof of Theorem 3an1rs
StepHypRef Expression
1 3an1rs.1 . . . 4 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
213exp1 1446 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
32com34 91 . 2 (𝜑 → (𝜓 → (𝜃 → (𝜒𝜏))))
433imp1 1441 1 (((𝜑𝜓𝜃) ∧ 𝜒) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  w3a 1072
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 197  df-an 385  df-3an 1074
This theorem is referenced by:  odf1o2  18188  neiptopnei  21138  cnextcn  22072
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