Theorem bnj832 35156

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

Hypotheses

Ref	Expression
bnj832.1	⊢ (𝜂 ↔ (𝜑 ∧ 𝜓))
bnj832.2	⊢ (𝜑 → 𝜏)

Assertion

Ref	Expression
bnj832	⊢ (𝜂 → 𝜏)

Proof of Theorem bnj832

Step	Hyp	Ref	Expression
1		bnj832.1	. 2 ⊢ (𝜂 ↔ (𝜑 ∧ 𝜓))
2		bnj832.2	. . 3 ⊢ (𝜑 → 𝜏)
3	2	adantr 485	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜏)
4	1, 3	sylbi 220	1 ⊢ (𝜂 → 𝜏)

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ wa 400

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 401

This theorem is used by:  bnj1379  35227  bnj605  35304  bnj908  35328  bnj1145  35390  bnj1442  35446  bnj1450  35447  bnj1489  35453  bnj1501  35464  bnj1523  35468