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Theorem 3an1rs 1270
Description: Swap conjuncts. (Contributed by NM, 16-Dec-2007.)
Hypothesis
Ref Expression
3an1rs.1 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
Assertion
Ref Expression
3an1rs (((𝜑𝜓𝜃) ∧ 𝜒) → 𝜏)

Proof of Theorem 3an1rs
StepHypRef Expression
1 3an1rs.1 . . . . . 6 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
21ex 448 . . . . 5 ((𝜑𝜓𝜒) → (𝜃𝜏))
323exp 1255 . . . 4 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
43com34 88 . . 3 (𝜑 → (𝜓 → (𝜃 → (𝜒𝜏))))
543imp 1248 . 2 ((𝜑𝜓𝜃) → (𝜒𝜏))
65imp 443 1 (((𝜑𝜓𝜃) ∧ 𝜒) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  w3a 1030
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 195  df-an 384  df-3an 1032
This theorem is referenced by:  odf1o2  17759  neiptopnei  20693  cnextcn  21628
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