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Mirrors > Home > MPE Home > Th. List > exp44 | Structured version Visualization version GIF version |
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.) |
Ref | Expression |
---|---|
exp44.1 | ⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜏) |
Ref | Expression |
---|---|
exp44 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exp44.1 | . . 3 ⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜏) | |
2 | 1 | exp32 424 | . 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜃 → 𝜏))) |
3 | 2 | expd 419 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 |
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 210 df-an 400 |
This theorem is referenced by: wefrc 5545 tz7.7 6239 oalimcl 8288 unbenlem 16461 rnelfm 22850 uspgr2wlkeqi 27735 1pthon2v 28236 spansncvi 29733 atom1d 30434 chirredlem3 30473 conway 33730 finminlem 34244 cvlcvr1 37090 lhpexle2lem 37760 trlord 38320 cdlemkid4 38685 dihord6apre 39007 dihglbcpreN 39051 |
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