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Theorem bnj770 29880
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 29871 . 2 ((𝜑𝜓𝜒𝜃) → 𝜏)
41, 3sylbi 205 1 (𝜂𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  w-bnj17 29798
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  df-bnj17 29799
This theorem is referenced by:  bnj1235  29922  bnj605  30024  bnj607  30033  bnj983  30068  bnj1110  30097  bnj1145  30108  bnj1256  30130  bnj1296  30136  bnj1450  30165
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