Theorem bnj1254 35305

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

Hypothesis

Ref	Expression
bnj1254.1	⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏))

Assertion

Ref	Expression
bnj1254	⊢ (𝜑 → 𝜏)

Proof of Theorem bnj1254

Step	Hyp	Ref	Expression
1		bnj1254.1	. 2 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏))
2		id 23	. . 3 ⊢ (𝜏 → 𝜏)
3	2	bnj708 35253	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏) → 𝜏)
4	1, 3	sylbi 220	1 ⊢ (𝜑 → 𝜏)

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ w-bnj17 35183

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-bnj17 35184

This theorem is used by:  bnj554  35395  bnj557  35397  bnj967  35441  bnj999  35454  bnj907  35463  bnj1118  35480  bnj1128  35486  bnj1253  35513  bnj1450  35546