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Theorem e12an 39477
Description: Conjunction form of e12 39476 (see syl6an 663). (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e12an.1 (   𝜑   ▶   𝜓   )
e12an.2 (   𝜑   ,   𝜒   ▶   𝜃   )
e12an.3 ((𝜓𝜃) → 𝜏)
Assertion
Ref Expression
e12an (   𝜑   ,   𝜒   ▶   𝜏   )

Proof of Theorem e12an
StepHypRef Expression
1 e12an.1 . 2 (   𝜑   ▶   𝜓   )
2 e12an.2 . 2 (   𝜑   ,   𝜒   ▶   𝜃   )
3 e12an.3 . . 3 ((𝜓𝜃) → 𝜏)
43ex 397 . 2 (𝜓 → (𝜃𝜏))
51, 2, 4e12 39476 1 (   𝜑   ,   𝜒   ▶   𝜏   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  (   wvd1 39310  (   wvd2 39318
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 197  df-an 383  df-vd1 39311  df-vd2 39319
This theorem is referenced by:  sstrALT2VD  39591
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