Theorem bnj832 30828

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 481	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜏)
4	1, 3	sylbi 207	1 ⊢ (𝜂 → 𝜏)

Syntax hints:   → wi 4   ↔ wb 196   ∧ wa 384

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 197  df-an 386

This theorem is referenced by:  bnj1379  30901  bnj605  30977  bnj908  31001  bnj1145  31061  bnj1442  31117  bnj1450  31118  bnj1489  31124  bnj1501  31135  bnj1523  31139