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Mirrors > Home > MPE Home > Th. List > ancoms | Structured version Visualization version GIF version |
Description: Inference commuting conjunction in antecedent. (Contributed by NM, 21-Apr-1994.) |
Ref | Expression |
---|---|
ancoms.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
ancoms | ⊢ ((𝜓 ∧ 𝜑) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancoms.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
2 | 1 | expcom 414 | . 2 ⊢ (𝜓 → (𝜑 → 𝜒)) |
3 | 2 | imp 407 | 1 ⊢ ((𝜓 ∧ 𝜑) → 𝜒) |
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