Theorem bnj1232 34786

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 34731	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏) → 𝜓)
3	1, 2	sylbi 217	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4   ↔ wb 206   ∧ w-bnj17 34669

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 207  df-an 396  df-3an 1088  df-bnj17 34670

This theorem is referenced by:  bnj605  34890  bnj607  34899  bnj944  34921  bnj969  34929  bnj970  34930  bnj1001  34942  bnj1110  34965  bnj1118  34967  bnj1128  34973  bnj1145  34976  bnj1311  35007