Theorem bnj835 34773

Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypotheses

Ref	Expression
bnj835.1	⊢ (𝜂 ↔ (𝜑 ∧ 𝜓 ∧ 𝜒))
bnj835.2	⊢ (𝜑 → 𝜏)

Assertion

Ref	Expression
bnj835	⊢ (𝜂 → 𝜏)

Proof of Theorem bnj835

Step	Hyp	Ref	Expression
1		bnj835.1	. 2 ⊢ (𝜂 ↔ (𝜑 ∧ 𝜓 ∧ 𝜒))
2		bnj835.2	. . 3 ⊢ (𝜑 → 𝜏)
3	2	3ad2ant1 1134	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜏)
4	1, 3	sylbi 217	1 ⊢ (𝜂 → 𝜏)

Syntax hints:   → wi 4   ↔ wb 206   ∧ w3a 1087

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 207  df-an 396  df-3an 1089

This theorem is referenced by:  bnj1219  34814  bnj1379  34844  bnj1175  35018  bnj1286  35033  bnj1280  35034  bnj1296  35035  bnj1398  35048  bnj1415  35052  bnj1417  35055  bnj1421  35056  bnj1442  35063  bnj1450  35064  bnj1452  35066  bnj1489  35070  bnj1312  35072  bnj1501  35081  bnj1523  35085