Theorem bnj1232 32779

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 32724	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏) → 𝜓)
3	1, 2	sylbi 216	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4   ↔ wb 205   ∧ w-bnj17 32661

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 397  df-3an 1088  df-bnj17 32662

This theorem is referenced by:  bnj605  32883  bnj607  32892  bnj944  32914  bnj969  32922  bnj970  32923  bnj1001  32935  bnj1110  32958  bnj1118  32960  bnj1128  32966  bnj1145  32969  bnj1311  33000