Theorem bnj1235 33815

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

Hypothesis

Ref	Expression
bnj1235.1	⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏))

Assertion

Ref	Expression
bnj1235	⊢ (𝜑 → 𝜒)

Proof of Theorem bnj1235

Step	Hyp	Ref	Expression
1		bnj1235.1	. 2 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏))
2		id 22	. 2 ⊢ (𝜒 → 𝜒)
3	1, 2	bnj770 33774	1 ⊢ (𝜑 → 𝜒)

Syntax hints:   → wi 4   ↔ wb 205   ∧ w-bnj17 33697

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 206  df-an 398  df-3an 1090  df-bnj17 33698

This theorem is referenced by:  bnj966  33955  bnj967  33956  bnj910  33959  bnj1006  33971  bnj1018g  33974  bnj1018  33975  bnj1110  33993  bnj1121  33996  bnj1311  34035