Theorem bnj835 34790

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 1133	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜏)
4	1, 3	sylbi 217	1 ⊢ (𝜂 → 𝜏)

Syntax hints:   → wi 4   ↔ wb 206   ∧ w3a 1086

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 1088

This theorem is referenced by:  bnj1219  34831  bnj1379  34861  bnj1175  35035  bnj1286  35050  bnj1280  35051  bnj1296  35052  bnj1398  35065  bnj1415  35069  bnj1417  35072  bnj1421  35073  bnj1442  35080  bnj1450  35081  bnj1452  35083  bnj1489  35087  bnj1312  35089  bnj1501  35098  bnj1523  35102