Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-com12 | Structured version Visualization version GIF version |
Description: Inference that swaps (commutes) antecedents in an implication. Copy of com12 32 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
wl-com12.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
wl-com12 | ⊢ (𝜓 → (𝜑 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wl-com12.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | wl-pm2.27 33257 | . 2 ⊢ (𝜓 → ((𝜓 → 𝜒) → 𝜒)) | |
3 | 1, 2 | wl-syl5 33247 | 1 ⊢ (𝜓 → (𝜑 → 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-luk1 33241 ax-luk2 33242 ax-luk3 33243 |
This theorem is referenced by: wl-pm2.21 33259 wl-imim2 33262 |
Copyright terms: Public domain | W3C validator |