Theorem bnj835 32258

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 1130	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜏)
4	1, 3	sylbi 220	1 ⊢ (𝜂 → 𝜏)

Syntax hints:   → wi 4   ↔ wb 209   ∧ w3a 1084

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 210  df-an 400  df-3an 1086

This theorem is referenced by:  bnj1219  32300  bnj1379  32330  bnj1175  32504  bnj1286  32519  bnj1280  32520  bnj1296  32521  bnj1398  32534  bnj1415  32538  bnj1417  32541  bnj1421  32542  bnj1442  32549  bnj1450  32550  bnj1452  32552  bnj1489  32556  bnj1312  32558  bnj1501  32567  bnj1523  32571