Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj240 | Structured version Visualization version GIF version |
Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj240.1 | ⊢ (𝜓 → 𝜓′) |
bnj240.2 | ⊢ (𝜒 → 𝜒′) |
Ref | Expression |
---|---|
bnj240 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜓′ ∧ 𝜒′)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj240.1 | . . . 4 ⊢ (𝜓 → 𝜓′) | |
2 | 1 | 3ad2ant1 1132 | . . 3 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → 𝜓′) |
3 | bnj240.2 | . . . 4 ⊢ (𝜒 → 𝜒′) | |
4 | 3 | 3ad2ant2 1133 | . . 3 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → 𝜒′) |
5 | 2, 4 | jca 512 | . 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → (𝜓′ ∧ 𝜒′)) |
6 | 5 | 3comr 1124 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜓′ ∧ 𝜒′)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 ∧ w3a 1086 |
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 206 df-an 397 df-3an 1088 |
This theorem is referenced by: bnj594 32889 bnj580 32890 bnj966 32921 bnj967 32922 |
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