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Theorem bnj707 30586
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj707.1 (𝜒𝜏)
Assertion
Ref Expression
bnj707 ((𝜑𝜓𝜒𝜃) → 𝜏)

Proof of Theorem bnj707
StepHypRef Expression
1 bnj258 30534 . . 3 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓𝜃) ∧ 𝜒))
21simprbi 480 . 2 ((𝜑𝜓𝜒𝜃) → 𝜒)
3 bnj707.1 . 2 (𝜒𝜏)
42, 3syl 17 1 ((𝜑𝜓𝜒𝜃) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1036  w-bnj17 30512
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 386  df-3an 1038  df-bnj17 30513
This theorem is referenced by:  bnj771  30595  bnj998  30787  bnj1001  30789  bnj1006  30790  bnj1053  30805  bnj1121  30814  bnj1030  30816
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