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Theorem bnj951 31184
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj951.1 (𝜏𝜑)
bnj951.2 (𝜏𝜓)
bnj951.3 (𝜏𝜒)
bnj951.4 (𝜏𝜃)
Assertion
Ref Expression
bnj951 (𝜏 → (𝜑𝜓𝜒𝜃))

Proof of Theorem bnj951
StepHypRef Expression
1 bnj951.1 . . 3 (𝜏𝜑)
2 bnj951.2 . . 3 (𝜏𝜓)
3 bnj951.3 . . 3 (𝜏𝜒)
41, 2, 33jca 1122 . 2 (𝜏 → (𝜑𝜓𝜒))
5 bnj951.4 . 2 (𝜏𝜃)
6 df-bnj17 31093 . 2 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓𝜒) ∧ 𝜃))
74, 5, 6sylanbrc 572 1 (𝜏 → (𝜑𝜓𝜒𝜃))
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1071  w-bnj17 31092
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 383  df-3an 1073  df-bnj17 31093
This theorem is referenced by:  bnj966  31352  bnj967  31353  bnj910  31356  bnj1006  31367  bnj1118  31390  bnj1177  31412
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