Theorem bnj1232 35353

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

Hypothesis

Ref	Expression
bnj1232.1	⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏))

Assertion

Ref	Expression
bnj1232	⊢ (𝜑 → 𝜓)

Proof of Theorem bnj1232

Step	Hyp	Ref	Expression
1		bnj1232.1	. 2 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏))
2		bnj642 35299	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏) → 𝜓)
3	1, 2	sylbi 220	1 ⊢ (𝜑 → 𝜓)

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ w-bnj17 35237

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 35238

This theorem is used by:  bnj605  35457  bnj607  35466  bnj944  35488  bnj969  35496  bnj970  35497  bnj1001  35509  bnj1110  35532  bnj1118  35534  bnj1128  35540  bnj1145  35543  bnj1311  35574