Theorem bnj1235 35501

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 23	. 2 ⊢ (𝜒 → 𝜒)
3	1, 2	bnj770 35461	1 ⊢ (𝜑 → 𝜒)

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ w-bnj17 35384

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 402  df-3an 1105  df-bnj17 35385

This theorem is used by:  bnj966  35641  bnj967  35642  bnj910  35645  bnj1006  35657  bnj1018g  35660  bnj1018  35661  bnj1110  35679  bnj1121  35682  bnj1311  35721