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Mirrors > Home > MPE Home > Th. List > Mathboxes > sbtd | Structured version Visualization version GIF version |
Description: A true statement is true upon substitution (deduction). A similar proof is possible for icht 44322. (Contributed by SN, 4-May-2024.) |
Ref | Expression |
---|---|
sbtd.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
sbtd | ⊢ (𝜑 → [𝑡 / 𝑥]𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbtd.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 1 | alrimiv 1929 | . 2 ⊢ (𝜑 → ∀𝑥𝜓) |
3 | stdpc4 2074 | . 2 ⊢ (∀𝑥𝜓 → [𝑡 / 𝑥]𝜓) | |
4 | 2, 3 | syl 17 | 1 ⊢ (𝜑 → [𝑡 / 𝑥]𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1537 [wsb 2070 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1912 |
This theorem depends on definitions: df-bi 210 df-sb 2071 |
This theorem is referenced by: (None) |
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