Theorem bnj1232 31391

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 31335	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏) → 𝜓)
3	1, 2	sylbi 209	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4   ↔ wb 198   ∧ w-bnj17 31272

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 199  df-an 386  df-3an 1110  df-bnj17 31273

This theorem is referenced by:  bnj605  31494  bnj607  31503  bnj944  31525  bnj969  31533  bnj970  31534  bnj1001  31545  bnj1110  31567  bnj1118  31569  bnj1128  31575  bnj1145  31578  bnj1311  31609