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Mirrors > Home > MPE Home > Th. List > Mathboxes > axfrege58b | Structured version Visualization version GIF version |
Description: If ∀𝑥𝜑 is affirmed, [𝑦 / 𝑥]𝜑 cannot be denied. Identical to stdpc4 2428. Justification for ax-frege58b 39151. (Contributed by RP, 28-Mar-2020.) |
Ref | Expression |
---|---|
axfrege58b | ⊢ (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | stdpc4 2428 | 1 ⊢ (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1599 [wsb 2011 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2055 ax-12 2163 ax-13 2334 |
This theorem depends on definitions: df-bi 199 df-an 387 df-ex 1824 df-sb 2012 |
This theorem is referenced by: (None) |
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