Theorem bnj1247 35205

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

Hypothesis

Ref	Expression
bnj1247.1	⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏))

Assertion

Ref	Expression
bnj1247	⊢ (𝜑 → 𝜃)

Proof of Theorem bnj1247

Step	Hyp	Ref	Expression
1		bnj1247.1	. 2 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏))
2		id 23	. 2 ⊢ (𝜃 → 𝜃)
3	1, 2	bnj771 35162	1 ⊢ (𝜑 → 𝜃)

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ w-bnj17 35084

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  df-3an 1104  df-bnj17 35085

This theorem is used by:  bnj1110  35379  bnj1128  35387  bnj1245  35411