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Mirrors > Home > MPE Home > Th. List > Mathboxes > anim12da | Structured version Visualization version GIF version |
Description: Conjoin antecedents and consequents in a deduction. (Contributed by Jeff Madsen, 16-Jun-2011.) |
Ref | Expression |
---|---|
anim12da.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
anim12da.2 | ⊢ ((𝜑 ∧ 𝜒) → 𝜏) |
Ref | Expression |
---|---|
anim12da | ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → (𝜃 ∧ 𝜏)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anim12da.1 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜃) | |
2 | anim12da.2 | . 2 ⊢ ((𝜑 ∧ 𝜒) → 𝜏) | |
3 | 1, 2 | anim12dan 882 | 1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → (𝜃 ∧ 𝜏)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 384 |
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 386 |
This theorem is referenced by: ghomco 33690 rngohomco 33773 rngoisocnv 33780 rngoisoco 33781 idlsubcl 33822 |
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