Theorem bnj835 32025

Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypotheses

Ref	Expression
bnj835.1	⊢ (𝜂 ↔ (𝜑 ∧ 𝜓 ∧ 𝜒))
bnj835.2	⊢ (𝜑 → 𝜏)

Assertion

Ref	Expression
bnj835	⊢ (𝜂 → 𝜏)

Proof of Theorem bnj835

Step	Hyp	Ref	Expression
1		bnj835.1	. 2 ⊢ (𝜂 ↔ (𝜑 ∧ 𝜓 ∧ 𝜒))
2		bnj835.2	. . 3 ⊢ (𝜑 → 𝜏)
3	2	3ad2ant1 1129	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜏)
4	1, 3	sylbi 219	1 ⊢ (𝜂 → 𝜏)

Syntax hints:   → wi 4   ↔ wb 208   ∧ w3a 1083

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 209  df-an 399  df-3an 1085

This theorem is referenced by:  bnj1219  32067  bnj1379  32097  bnj1175  32271  bnj1286  32286  bnj1280  32287  bnj1296  32288  bnj1398  32301  bnj1415  32305  bnj1417  32308  bnj1421  32309  bnj1442  32316  bnj1450  32317  bnj1452  32319  bnj1489  32323  bnj1312  32325  bnj1501  32334  bnj1523  32338