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Mirrors > Home > MPE Home > Th. List > Mathboxes > pm10.542 | Structured version Visualization version GIF version |
Description: Theorem *10.542 in [WhiteheadRussell] p. 156. (Contributed by Andrew Salmon, 24-May-2011.) |
Ref | Expression |
---|---|
pm10.542 | ⊢ (∀𝑥(𝜑 → (𝜒 → 𝜓)) ↔ (𝜒 → ∀𝑥(𝜑 → 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi2.04 392 | . . 3 ⊢ ((𝜑 → (𝜒 → 𝜓)) ↔ (𝜒 → (𝜑 → 𝜓))) | |
2 | 1 | albii 1827 | . 2 ⊢ (∀𝑥(𝜑 → (𝜒 → 𝜓)) ↔ ∀𝑥(𝜒 → (𝜑 → 𝜓))) |
3 | 19.21v 1947 | . 2 ⊢ (∀𝑥(𝜒 → (𝜑 → 𝜓)) ↔ (𝜒 → ∀𝑥(𝜑 → 𝜓))) | |
4 | 2, 3 | bitri 278 | 1 ⊢ (∀𝑥(𝜑 → (𝜒 → 𝜓)) ↔ (𝜒 → ∀𝑥(𝜑 → 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 209 ∀wal 1541 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 |
This theorem depends on definitions: df-bi 210 df-ex 1788 |
This theorem is referenced by: (None) |
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