Theorem bnj1254 31415

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypothesis

Ref	Expression
bnj1254.1	⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏))

Assertion

Ref	Expression
bnj1254	⊢ (𝜑 → 𝜏)

Proof of Theorem bnj1254

Step	Hyp	Ref	Expression
1		bnj1254.1	. 2 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏))
2		id 22	. . 3 ⊢ (𝜏 → 𝜏)
3	2	bnj708 31361	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏) → 𝜏)
4	1, 3	sylbi 209	1 ⊢ (𝜑 → 𝜏)

Syntax hints:   → wi 4   ↔ wb 198   ∧ w-bnj17 31290

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 199  df-an 387  df-bnj17 31291

This theorem is referenced by:  bnj554  31504  bnj557  31506  bnj967  31550  bnj999  31562  bnj907  31570  bnj1118  31587  bnj1128  31593  bnj1253  31620  bnj1450  31653