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Mirrors > Home > NFE Home > Th. List > an4s | GIF version |
Description: Inference rearranging 4 conjuncts in antecedent. (Contributed by NM, 10-Aug-1995.) |
Ref | Expression |
---|---|
an4s.1 | ⊢ (((φ ∧ ψ) ∧ (χ ∧ θ)) → τ) |
Ref | Expression |
---|---|
an4s | ⊢ (((φ ∧ χ) ∧ (ψ ∧ θ)) → τ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | an4 797 | . 2 ⊢ (((φ ∧ χ) ∧ (ψ ∧ θ)) ↔ ((φ ∧ ψ) ∧ (χ ∧ θ))) | |
2 | an4s.1 | . 2 ⊢ (((φ ∧ ψ) ∧ (χ ∧ θ)) → τ) | |
3 | 1, 2 | sylbi 187 | 1 ⊢ (((φ ∧ χ) ∧ (ψ ∧ θ)) → τ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 358 |
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 177 df-an 360 |
This theorem is referenced by: an42s 800 anandis 803 anandirs 804 2mo 2282 fnun 5190 f1co 5265 f1oun 5305 f1oco 5309 fntxp 5805 fnpprod 5844 f1opprod 5845 enprmaplem3 6079 sbthlem3 6206 fnfrec 6321 |
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