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Theorem bnj770 31161
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj770.1 (𝜂 ↔ (𝜑𝜓𝜒𝜃))
bnj770.2 (𝜓𝜏)
Assertion
Ref Expression
bnj770 (𝜂𝜏)

Proof of Theorem bnj770
StepHypRef Expression
1 bnj770.1 . 2 (𝜂 ↔ (𝜑𝜓𝜒𝜃))
2 bnj770.2 . . 3 (𝜓𝜏)
32bnj706 31152 . 2 ((𝜑𝜓𝜒𝜃) → 𝜏)
41, 3sylbi 207 1 (𝜂𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  w-bnj17 31082
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  df-bnj17 31083
This theorem is referenced by:  bnj1235  31203  bnj605  31305  bnj607  31314  bnj983  31349  bnj1110  31378  bnj1145  31389  bnj1256  31411  bnj1296  31417  bnj1450  31446
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