Theorem bnj832 30082

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 480	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜏)
4	1, 3	sylbi 206	1 ⊢ (𝜂 → 𝜏)

Syntax hints:   → wi 4   ↔ wb 195   ∧ wa 383

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 196  df-an 385

This theorem is referenced by:  bnj1379  30155  bnj605  30231  bnj908  30255  bnj1145  30315  bnj1442  30371  bnj1450  30372  bnj1489  30378  bnj1501  30389  bnj1523  30393